\letter {}
  (Near-)Additive Magma Categories, \indexit{558}
  (Near-)Additive Magma Generation, \indexit{559}
  `+', 48
  `-', 48
  `-A', 30
  `-B', 30
  `-C', 31
  `-D', 30
  `-K', 29
  `-L', 29
  `-M', 30
  `-N', 30
  `-O', 30
  `-P', 31
    \sub on Macintosh, 31
  `-R', 29
  `-T', 31
  `-U', 31
  `-W', 31
    \sub on Macintosh, 32
  `-X', 31
  `-Y', 31
  `-a', 30
    \sub on Macintosh, 32
  `-b', 27
  `-e', 27
    \sub on Macintosh, 32
  `-f', 27
    \sub on Macintosh, 32
  `-g', 28
  `-g -g', 28
  `-h', 27
  `-i', 31
  `-l', 29
  `-m', 28
  `-n', 28
    \sub on Macintosh, 32
  `-o', 28
    \sub on Macintosh, 32
  `-p', 31
  `-q', 27
  `-r', 29
  `-x', 28
  `-y', 28
  `-z', 31
    \sub on Macintosh, 31
  `.gaprc', 33
  `/', 48
    \sub for character tables, 734
  `\*', 48
    \sub for character tables, 734
  `\\\char 39', 252
  `\\XYZ', 252
  `\\\"', 252
  `\\\\', 252
  `\\b', 252
  `\\c', 252
  `\\in', operation for testing membership, 277
  `\\n', 252
  `\\r', 252
  `{\accent 94 }', 48
    \sub for class functions, 773
  1-Cohomology, \indexit{380}
  2-Cohomology and Extensions, \indexit{459}
\letter A
  `AbelianGroup', 512
  `AbelianInvariants', for character tables, 736
    \sub for groups, 369
  Abelian Invariants for Subgroups, \indexit{479}
  `AbelianInvariantsMultiplier', 383
  `AbelianInvariantsNormalClosureFpGroup', 479
  `Abelian\-Invariants\-Normal\-Closure\-Fp\-Group\-Rrs', 479
  `AbelianInvariantsOfList', 244
  `AbelianInvariantsSubgroupFpGroup', 479
  `AbelianInvariantsSubgroupFpGroupMtc', 479
  `AbelianInvariantsSubgroupFpGroupRrs', 479
  `AbelianNumberField', 592
  abelian number field, 594
  abelian number fields, canonicalbasis, 595
  abelian number fields, Galois group, 597
  `AbelianSubfactorAction', 405
  About Group Actions, \indexit{397}
  `AbsInt', 127
  `AbsoluteIrreducibleModules', 754
  `AbsoluteValue', 159
  absolute value of an integer, 127
  `AbsolutIrreducibleModules', 754
  abstract word, 326
  `AbstractWordTietzeWord', 488
  accessing, list elements, 175
    \sub record elements, 263
  Accessing a Module, \indexit{698}
  Accessing Record Elements, \indexit{263}
  Accessing Subgroups via Tables of Marks, \indexit{719}
  `AClosestVectorCombinationsMatFFEVecFFE', 220
  `AClosest\-Vector\-Combinations\-Mat\-FFEVec\-FFECoords', 220
  `ActingAlgebra', 635
  `ActingDomain', 409
  Acting OnRight and OnLeft, \indexit{435}
  `Action', 404
  action, by conjugation, 398
    \sub on blocks, 398
    \sub on sets, 398
  `ActionHomomorphism', 403
  Action of a group on itself, \indexit{405}
  Action on Subfactors Defined by a Pcgs, \indexit{450}
  actions, 398
  Actions of Matrix Groups, \indexit{431}
  `ActorOfExternalSet', 411
  `Add', 178
  add, an element to a set, 198
  `AddCoeffs', 218
  `AddGenerator', 490
  `AddGenerators', 346
  `AddGeneratorsExtendSchreierTree', 427
  addition, 48
    \sub list and non-list, 187
    \sub matrices, 224
    \sub matrix and scalar, 224
    \sub operation, 297
    \sub rational functions, 671
    \sub scalar and matrix, 224
    \sub scalar and matrix list, 226
    \sub scalar and vector, 216
    \sub vector and scalar, 216
    \sub vectors, 216
  Additive Arithmetic for Lists, \indexit{187}
  `AdditiveInverse', 295
  `AdditiveInverseAttr', 295
  `AdditiveInverseImmutable', 295
  `AdditiveInverseMutable', 295
  `AdditiveInverseOp', 295
  `AdditiveInverseSameMutability', 295
  `AdditiveInverseSM', 295
  `AdditiveNeutralElement', 560
  `AddRelator', 490
  `AddRowVector', 218
  `AddRule', 346
  `AddRuleReduced', 346
  `AddSet', 198
  `AdjointAssociativeAlgebra', 652
  `AdjointBasis', 624
  `AdjointMatrix', 652
  `AdjointModule', 637
  Advanced Features of GAP, \indexit{30}
  Advanced List Manipulations, \indexit{206}
  Advanced Methods for Dixon-Schneider Calculations, \indexit{755}
  `AffineAction', 450
  `AffineActionLayer', 450
  `AffineOperation', 450
  `AffineOperationLayer', 450
  `Agemo', 366
  `Algebra', 615
  `AlgebraByStructureConstants', 618
  `AlgebraGeneralMappingByImages', 629
  `AlgebraHomomorphismByImages', 629
  `AlgebraHomomorphismByImagesNC', 629
  `AlgebraicExtension', 692
  `AlgebraWithOne', 615
  `AlgebraWithOneGeneralMappingByImages', 630
  `AlgebraWithOneHomomorphismByImages', 630
  `AlgebraWithOneHomomorphismByImagesNC', 630
  `AllBlocks', 408
  `AllIrreducibleSolvableGroups', 530
  `All<Library>Groups', 518
  `AllPrimitiveGroups', 518
  `AllSmallGroups', 521
  `AllTransitiveGroups', 518
  `Alpha', 825
  `AlternatingGroup', 512
  `and', 171
    \sub for filters, 117, 172
  An Example of Advanced Dixon-Schneider Calculations, \indexit{756}
  `ANFAutomorphism', 597
  `AntiSymmetricParts', 790
  antisymmetric relation, 316
  `Append', 179
  `AppendTo', 95
    \sub for streams, 101
  Apple, 841, 842
  `ApplicableMethod', 78
  ApplicableMethod, \indexit{78}
  `ApplicableMethodTypes', 78
  `Apply', 201
  `ApplySimpleReflection', 649
  `ApproximateSuborbitsStabilizerPermGroup', 425
  `ARCH_IS_MAC', 35
  `ARCH_IS_UNIX', 35
  `ARCH_IS_WINDOWS', 35
  `arg', special function argument, 46, 56
  Arithmetic for External Representations of Polynomials, \indexit{691}
  Arithmetic for Lists, \indexit{185}
  Arithmetic Operations for Class Functions, \indexit{772}
  Arithmetic Operations for Elements, \indexit{297}
  Arithmetic Operations for General Mappings, \indexit{310}
  Arithmetic Operators, \indexit{48}
  `Arrangements', 149
  arrow notation for functions, 57
  `AsAlgebra', 624
  `AsAlgebraWithOne', 625
  `AsBinaryRelationOnPoints', 317
  `AsBlockMatrix', 240
  `AscendingChain', 372
  `AsDivisionRing', 579
  `AsDuplicateFreeList', 200
  `AsField', 579
  `AsFreeLeftModule', 576
  `AsGroup', 351
  `AsGroupGeneralMappingByImages', 387
  `AsLeftIdeal', 566
  `AsLeftModule', 574
  `AsList', 272
  `AsMagma', 321
  `AsMonoid', 546
  `AsPolynomial', 673
  `AsRightIdeal', 566
  `AsRing', 563
  `AsSemigroup', 539
  `Assert', 81
  `AssertionLevel', 81
  Assertions, \indexit{81}
  `AsSet', 272
  `AssignGeneratorVariables', 333
  assignment, to a list, 177
    \sub to a record, 263
    \sub variable, 50
  Assignments, \indexit{50}
  `AssignNiceMonomorphismAutomorphismGroup', 393
  `AssociatedPartition', 154
  `AssociatedReesMatrixSemigroupOfDClass', 545
  `Associates', 569
  associativity, 48
  `AssocWordByLetterRep', 338
  `AsSortedList', 272
  `AsSSortedList', 272
  `As<Struct>', 289
  `AsSubalgebra', 625
  `AsSubalgebraWithOne', 625
  `AsSubgroup', 352
  `AsSubgroupOfWholeGroupByQuotient', 477
  `AsSubmagma', 322
  `AsSubmonoid', 546
  `AsSubsemigroup', 539
  `AsSubspace', 600
  `AsSub<struct>', 292
  `AsTransformation', 556
  `AsTransformationNC', 556
  `AsTwoSidedIdeal', 566
  `AsVectorSpace', 599
  at exit functions, 73
  ATLAS Irrationalities, \indexit{161}
  `AtlasIrrationality', 163
  atomic irrationalities, 161
  Attributes, \indexit{121}
  Attributes and Operations for Algebras, \indexit{623}
  Attributes and Properties for (Near-)Additive Magmas, \indexit{560}
  Attributes and Properties for Collections, \indexit{273}
  Attributes and Properties for Magmas, \indexit{323}
  Attributes and Properties for Matrix Groups, \indexit{430}
  Attributes and Properties of Character Tables, \indexit{734}
  Attributes and Properties of Elements, \indexit{293}
  Attributes of and Operations on Equivalence Relations, \indexit{318}
  Attributes of Tables of Marks, \indexit{709}
  `AttributeValueNotSet', 122
  `AugmentationIdeal', 664
  `AugmentedCosetTableInWholeGroup', 471
  `AugmentedCosetTableMtc', 471
  `AugmentedCosetTableRrs', 471
  Augmented Coset Tables and Rewriting, \indexit{471}
  automatic loading of gap packages, 846
  `AutomorphismDomain', 392
  `AutomorphismGroup', 392
    \sub for groups with pcgs, 451
  automorphism group, of number fields, 597
  Automorphisms and Equivalence of Character Tables, \indexit{763}
  `AutomorphismsOfTable', 738
\letter B
  $b_N$, 161
  backslash character, 252
  backspace character, 252
  `Backtrace', GAP3 name for `Where', 70
  Backtrack, \indexit{427}
  `BANNER', 851
  `BaseFixedSpace', 231
  `BaseIntersectionIntMats', 241
  `BaseIntMat', 241
  `BaseMat', 234
  `BaseMatDestructive', 234
  `BaseOfGroup', 424
  `BaseOrthogonalSpaceMat', 234
  Bases of Vector Spaces, \indexit{601}
  `BaseStabChain', 424
  `BaseSteinitzVectors', 234
  Basic Actions, \indexit{398}
  Basic Groups, \indexit{511}
  Basic Operations for Class Functions, \indexit{770}
  Basic Operations for Lists, \indexit{175}
  `BasicWreathProductOrdering', 285
  `Basis', 602
  `BasisNC', 602
  `BasisVectors', 603
  `Bell', 148
  `Bernoulli', 148
  `BestQuoInt', 129
  `BestSplittingMatrix', 755
  `BiAlgebraModule', 633
  `BiAlgebraModuleByGenerators', 633
  `BilinearFormMat', 648
  binary relation, 315
  `BinaryRelationByElements', 315
  `BinaryRelationOnPoints', 317
  `BinaryRelationOnPointsNC', 317
  Binary Relations on Points, \indexit{317}
  `BinaryRelationTransformation', 557
  `BindGlobal', 45
  `Binomial', 147
  blank, 41
  `BlistList', 211
  Block Matrices, \indexit{240}
  `BlockMatrix', 240
  `Blocks', 408
  `BlocksInfo', 743
  Block Systems, \indexit{408}
  `BlownUpMat', 236
  `BlownUpVector', 236
  `BlowUpIsomorphism', 431
  BNF, 59
  body, 55
  `BombieriNorm', 679
  Boolean Lists Representing Subsets, \indexit{211}
  bound, 43
  Brauer character, 777
  `BrauerCharacterValue', 800
  `BrauerTable', 728
  `BrauerTableOp', 728
  `BravaisGroup', 434
  `BravaisSubgroups', 434
  `BravaisSupergroups', 434
  Break, \indexit{55}
  break loop message, 70
  Break Loops, \indexit{67}
  `break' statement, 55
  browsing backwards, 22
  browsing backwards one chapter, 23
  browsing forward, 22
  browsing forward one chapter, 23
  browsing the next section browsed, 23
  browsing the previous section browsed, 23
  Browsing through the Sections, \indexit{22}
  bug reports, see If Things Go Wrong, 838
  Building new orderings, \indexit{281}
\letter C
  $c_N$, 161
  Calculating with Group Automorphisms, \indexit{393}
  Calendar Arithmetic, \indexit{259}
  `CallFuncList', 62
  Calling a function with a list argument that is interpreted as several arguments, \indexit{62}
  Cancellation Tests for Rational Functions, \indexit{691}
  `CanComputeIndex', 384
  `CanComputeIsSubset', 384
  `CanComputeSize', 384
  `CanComputeSizeAnySubgroup', 384
  candidates, for permutation characters, 793, 796
  `CanEasilyCompareElements', 296
  `CanEasilyCompareElementsFamily', 296
  `CanEasilyComputePcgs', 437
  `CanEasilySortElements', 296
  `CanEasilySortElementsFamily', 296
  `CanEasilyTestMembership', 384
  `CanonicalBasis', 602
  canonical basis, for matrix spaces, 609
    \sub for row spaces, 609
  `CanonicalGenerators', 648
  `CanonicalPcElement', 439
  `CanonicalPcgs', 442
  `CanonicalPcgsByGeneratorsWithImages', 444
  `Canonical\-Representative\-Determinator\-Of\-External\-Set', 411
  `CanonicalRepresentativeOfExternalSet', 411
  `CanonicalRightCosetElement', 358
  Carmichael's lambda function, 139
  carriage return character, 252
  `CartanMatrix', 647
  `CartanSubalgebra', 644
  `Cartesian', 202
  Categories, \indexit{118}
  Categories and Properties of Algebras, \indexit{622}
  Categories for Streams and the StreamsFamily, \indexit{97}
  Categories of Associative Words, \indexit{331}
  Categories of Matrices, \indexit{223}
  `CategoriesOfObject', 120
  Categories of Words and Nonassociative Words, \indexit{326}
  `CategoryCollections', 269
  `Center', 324
  center, 323
  `CentralCharacter', 781
  central character, 781
  `CentralIdempotentsOfAlgebra', 627
  centraliser, 323
  `Centralizer', 323
    \sub for groups with pcgs, 451
  `CentralizerInGLnZ', 434
  `CentralizerModulo', 373
  `CentralizerSizeLimitConsiderFunction', 452
  `CentralNormalSeriesByPcgs', 446
  `Centre', 324
    \sub for groups with pcgs, 451
  centre, of a character, 780
  `CentreOfCharacter', 780
  `CF', 592
  `ChangeStabChain', 426
  Changing Presentations, \indexit{490}
  Changing the Help Viewer, \indexit{23}
  Changing the Representation, \indexit{290}
  Changing the Structure, \indexit{289}
  `CHAR_INT', 258
  `CHAR_SINT', 258
  `Character', 775
  Character Conversion, \indexit{258}
  `CharacterDegrees', 734
  Character Degrees and Derived Length, \indexit{825}
  `Characteristic', 293
  characteristic, for class functions, 774
  `CharacteristicPolynomial', 235
  characteristic polynomial, for field elements, 581
  `CharacterNames', 738
  `CharacterParameters', 739
  characters, 768
    \sub permutation, 793, 796
    \sub symmetrizations of, 790
  `CharacterTable', 728
  Character Table Categories, \indexit{730}
  `CharacterTableDirectProduct', 758
  `CharacterTableFactorGroup', 759
  `CharacterTableIsoclinic', 760
  `CharacterTableRegular', 729
  character tables, 727
    \sub access to, 727
    \sub calculate, 727
    \sub infix operators, 734
    \sub of groups, 727
  `CharacterTableWithSortedCharacters', 761
  `CharacterTableWithSortedClasses', 761
  `CharacterTableWreathSymmetric', 760
  character value, of group element using powering operator, 773
  `CharsFamily', 254
  `CheapFactorsInt', 134
  `CheckFixedPoints', 814
  `CheckForHandlingByNiceBasis', 614
  `CheckPermChar', 821
  `ChevalleyBasis', 646
  `ChiefNormalSeriesByPcgs', 447
  `ChiefSeries', 370
  `ChiefSeriesThrough', 370
  `ChiefSeriesUnderAction', 370
  `ChineseRem', 130
  Chinese remainder, 131
  `Chomp', 257
  `CIUnivPols', 671
  `ClassElementLattice', 375
  classes, real, 740
  `ClassesSolvableGroup', 451
  `ClassFunction', 775
  class function, 768
  class function objects, 768
  class functions, 811
    \sub as ring elements, 772
  `ClassFunctionSameType', 776
  Class Fusions between Character Tables, \indexit{806}
  Classical Groups, \indexit{513}
  `ClassMultiplicationCoefficient', for character tables, 747
  class multiplication coefficient, 747, 748
  `ClassNames', 738
  `ClassNamesTom', 710
  `ClassOrbit', 740
  `ClassParameters', 739
  `ClassPermutation', 762
  `ClassPositionsOfAgemo', 740
  `ClassPositionsOfCentre', for characters, 780
    \sub for character tables, 740
  `ClassPositionsOfDerivedSubgroup', 741
  `Class\-Positions\-Of\-Direct\-Product\-Decompositions', 741
  `ClassPositionsOfElementaryAbelianSeries', 741
  `ClassPositionsOfFittingSubgroup', 741
  `ClassPositionsOfKernel', 779
  `ClassPositionsOfLowerCentralSeries', 741
  `ClassPositionsOfMaximalNormalSubgroups', 740
  `ClassPositionsOfMinimalNormalSubgroups', 740
  `ClassPositionsOfNormalClosure', 741
  `ClassPositionsOfNormalSubgroup', 766
  `ClassPositionsOfNormalSubgroups', 740
  `ClassPositionsOfSupersolvableResiduum', 741
  `ClassPositionsOfUpperCentralSeries', 741
  `ClassRoots', 740
  `ClassStructureCharTable', 747
  `ClassTypesTom', 709
  `CleanedTailPcElement', 440
  `ClearCacheStats', 84
  `ClearProfile', 83
  clone, an object, 113
  `CloseMutableBasis', 607
  `CloseStream', 98
  `ClosureGroup', 354
  `ClosureGroupAddElm', 354
  `ClosureGroupCompare', 354
  `ClosureGroupDefault', 354
  `ClosureGroupIntest', 354
  `ClosureLeftModule', 575
  `ClosureNearAdditiveGroup', 561
  Closure Operations and Other Constructors, \indexit{317}
  `ClosureRing', 563
  Closures of (Sub)groups, \indexit{354}
  `Closure<Struct>', 289
  `ClosureSubgroup', 354
  `ClosureSubgroupNC', 354
  `Coboundaries', 657
  `Cochain', 656
  `CochainSpace', 656
  `Cocycles', 657
  cocycles, 380
  `CodePcGroup', 462
  `CodePcgs', 462
  Coding a Pc Presentation, \indexit{462}
  coefficient, binomial, 147
  Coefficient List Arithmetic, \indexit{218}
  `Coefficients', 603
  coefficients, for cyclotomics, 159
  `CoefficientsAndMagmaElements', 665
  `CoefficientsFamily', 688
  `CoefficientsMultiadic', 130
  `CoefficientsOfLaurentPolynomial', 680
  `CoefficientsOfUnivariatePolynomial', 673
  `Coefficients\-Of\-Univariate\-Rational\-Function', 673
  `CoefficientsQadic', 130
  `CoefficientsRing', 681
  `CoeffsCyc', 159
  `CoeffsMod', 219
  cohomology, 380
  `COHORTS_PRIMITIVE_GROUPS', 528
  `CoKernelOfAdditiveGeneralMapping', 312
  `CoKernelOfMultiplicativeGeneralMapping', 311
  `CollapsedMat', 817
  `Collected', 200
  Collection Families, \indexit{268}
  `CollectionsFamily', 268
  Coloring the Prompt and Input, \indexit{38}
  `ColorPrompt', 38
  `ColumnIndexOfReesMatrixSemigroupElement', 545
  `Column\-Index\-Of\-Rees\-Zero\-Matrix\-Semigroup\-Element', 545
  `Combinations', 149
  Combinations, Arrangements and Tuples, \indexit{149}
  `CombinatorialCollector', 456
  Combinatorial Numbers, \indexit{147}
  `Comm', 297
    \sub for words, 335
  Command Line Options, \indexit{27}
  comments, 41
  `CommutativeDiagram', 814
  `CommutatorFactorGroup', 373
  `CommutatorLength', 364
    \sub for character tables, 736
  `CommutatorSubgroup', 363
  `Compacted', 199
  `CompanionMat', 237
  `CompareVersionNumbers', 849
  comparison, fp semigroup elements, 551
    \sub operation, 296
    \sub rational functions, 671
  Comparison of Associative Words, \indexit{334}
  Comparison of Class Functions, \indexit{771}
  Comparison of Elements of Finitely Presented Groups, \indexit{465}
  Comparison of Elements of Finitely Presented Semigroups, \indexit{551}
  Comparison of Permutations, \indexit{413}
  Comparison of Rational Functions, \indexit{671}
  Comparison of Words, \indexit{328}
  Comparison Operations for Elements, \indexit{296}
  Comparisons, \indexit{47}
  comparisons, of booleans, 170
    \sub of lists, 184
  Comparisons of Booleans, \indexit{170}
  Comparisons of Cyclotomics, \indexit{161}
  Comparisons of Lists, \indexit{184}
  Comparisons of Records, \indexit{265}
  Comparisons of Strings, \indexit{254}
  `CompatibleConjugacyClasses', 733
  `CompatiblePairs', 460
  Compilation, \indexit{833}
  Compiling Library Code, \indexit{36}
  `Complementclasses', 363
  `ComplementclassesEA', 382
  `ComplementIntMat', 242
  `ComplementSystem', 366
  Completion Files, \indexit{34}
  `ComplexConjugate', 164
    \sub for class functions, 774
  `ComplexificationQuat', 619
  Components of a Dixon Record, \indexit{756}
  `CompositionMapping', 305
    \sub for Frobenius automorphisms, 589
  `CompositionMapping2', 305
  `CompositionMaps', 811
  `CompositionOfStraightLinePrograms', 342
  `CompositionSeries', 370
    \sub for groups with pcgs, 451
  `ComputedBrauerTables', 728
  `ComputedClassFusions', 807
  `ComputedIndicators', 746
  `ComputedIsPSolvableCharacterTables', 746
  `ComputedPowerMaps', 803
  `ComputedPrimeBlockss', 742
  Computing a Pcgs, \indexit{437}
  Computing a Permutation Representation, \indexit{417}
  Computing Pc Groups, \indexit{457}
  Computing Possible Permutation Characters, \indexit{796}
  Computing the Irreducible Characters of a Group, \indexit{751}
  `Concatenation', 199
  concatenation, of lists, 199
  `Conductor', 159
  `ConfluentRws', 346
  `Congruences', for character tables, 819
  Congruences for semigroups, \indexit{542}
  `ConjugacyClass', 360
  Conjugacy Classes, \indexit{360}
  `ConjugacyClasses', attribute, 360
    \sub for character tables, 732
    \sub for groups with pcgs, 451
    \sub for linear groups, 517
  `ConjugacyClassesByOrbits', 361
  `ConjugacyClassesByRandomSearch', 361
  Conjugacy Classes in Classical Groups, \indexit{517}
  Conjugacy Classes in Solvable Groups, \indexit{451}
  `ConjugacyClassesMaximalSubgroups', 374
  `ConjugacyClassesPerfectSubgroups', 377
  `ConjugacyClassesSubgroups', 374
  `ConjugacyClassSubgroups', 374
  conjugate, matrix, 225
    \sub of a word, 335
  `ConjugateDominantWeight', 649
  `ConjugateDominantWeightWithWord', 649
  `ConjugateGroup', 351
  `Conjugates', 582
  `ConjugateSubgroup', 353
  `ConjugateSubgroups', 353
  conjugation, 398
  `ConjugatorAutomorphism', 391
  `ConjugatorAutomorphismNC', 391
  `ConjugatorIsomorphism', 390
  `ConjugatorOfConjugatorIsomorphism', 391
  `ConnectGroupAndCharacterTable', 732
  `ConsiderKernels', 819
  `ConsiderSmallerPowerMaps', 820
  `ConsiderStructureConstants', 811
  `ConsiderTableAutomorphisms', 822
  `ConstantTimeAccessList', 195
  constituent, of a group character, 778
  `ConstituentsCompositionMapping', 306
  `ConstituentsOfCharacter', 779
  Constructing Algebras as Free Algebras, \indexit{616}
  Constructing Algebras by Generators, \indexit{615}
  Constructing Algebras by Structure Constants, \indexit{617}
  Constructing Character Tables from Others, \indexit{758}
  Constructing Domains, \indexit{288}
  Constructing Lie algebras, \indexit{641}
  Constructing Pc Groups, \indexit{455}
  Constructing Subdomains, \indexit{292}
  Constructing Tables of Marks, \indexit{704}
  Constructing Vector Spaces, \indexit{599}
  Construction of Abelian Number Fields, \indexit{592}
  Construction of Stabilizer Chains, \indexit{422}
  Constructors for Basic Groups, \indexit{517}
  `ContainedCharacters', 818
  `ContainedDecomposables', 818
  `ContainedMaps', 813
  `ContainedPossibleCharacters', 816, 817
  `ContainedPossibleVirtualCharacters', 816, 817
  `ContainedSpecialVectors', 816, 817
  `ContainedTom', 714
  `ContainingTom', 714
  `ContinuedFractionApproximationOfRoot', 143
  `ContinuedFractionExpansionOfRoot', 143
  Continued Fractions, \indexit{143}
  `continue' statement, 55
  Conventions for Character Tables, \indexit{731}
  convert, to a string, 253
  Converting Groups to Finitely Presented Groups, \indexit{473}
  `ConvertToCharacterTable', 730
  `ConvertToCharacterTableNC', 730
  `ConvertToMatrixRep', 237
  `ConvertToMatrixRepNC', 237
  `ConvertToRangeRep', 209
  `ConvertToStringRep', 253
  `ConvertToTableOfMarks', 708
  `ConvertToVectorRep', 217
  `ConvertToVectorRepNC', 217
  `ConwayPolynomial', 589
  Conway Polynomials, \indexit{589}
  coprime, 48
  copy, 113
    \sub an object, 113
  `COPY_LIST_ENTRIES', 179
  `CopyOptionsDefaults', 426
  Copyrights, \indexit{845}
  `CopyStabChain', 426
  `Core', 362
  `CorrespondingGeneratorsByModuloPcgs', 444
  coset, 357
  `CosetLeadersMatFFE', 220
  Cosets, \indexit{357}
  `CosetTable', 467
  `CosetTableBySubgroup', 468
  `CosetTableDefaultLimit', 469
  `CosetTableDefaultMaxLimit', 469
  `CosetTableFromGensAndRels', 468
  `CosetTableInWholeGroup', 471
  `CosetTableOfFpSemigroup', 554
  Coset Tables and Coset Enumeration, \indexit{467}
  Coset tables for subgroups in the whole group, \indexit{471}
  `CosetTableStandard', 470
  CRC, 37
  `CrcFile', 95
    \sub example, 37
  CRC Numbers, \indexit{37}
  `CreateCompletionFiles', 34
  `CreateCompletionFilesPkg', 850
  Creating Character Tables, \indexit{727}
  Creating Class Functions from Values Lists, \indexit{775}
  Creating Class Functions using Groups, \indexit{776}
  Creating Finite Fields, \indexit{587}
  Creating Finitely Presented Groups, \indexit{464}
  Creating Finitely Presented Semigroups, \indexit{550}
  Creating Group Homomorphisms, \indexit{385}
  Creating Groups, \indexit{350}
  Creating Mappings, \indexit{305}
  Creating Permutations, \indexit{415}
  Creating Presentations, \indexit{482}
  Creation of Algebraic Extensions, \indexit{692}
  Creation of Rational Functions, \indexit{690}
  Credit, \indexit{21}
  `CrystGroupDefaultAction', 435
  `Cycle', 406
  `CycleLength', 406
  `CycleLengths', 406
  `Cycles', 406
  `CycleStructureClass', 780
  `CycleStructurePerm', 414
  `CyclicExtensionsTom', 714
  `CyclicGroup', 511
  `CyclotomicField', 592
  cyclotomic field elements, 157
  cyclotomic fields, canonicalbasis, 595
  `CyclotomicPolynomial', 677
  Cyclotomic Polynomials, \indexit{677}
  `Cyclotomics', 157
  cyclotomics, defaultfield, 593
\letter D
  $d_N$, 161
  Darstellungsgruppe, see `EpimorphismSchurCover', 383
  `DataType', 125
  data type, unknown, 168
  `DayDMY', 260
  `DaysInMonth', 259
  `DaysInYear', 259
  Debugging Recursion, \indexit{85}
  DEC, 245
  `DeclareAutoPackage', 850
  `DeclareHandlingByNiceBasis', 613
  `DeclareInfoClass', 80
  `DeclarePackage', 850
  `DeclarePackageAutoDocumentation', 850
  `DeclarePackageDocumentation', 850
  `DecodeTree', 500
  DecodeTree, \indexit{500}
  decompose, a group character, 778
  `DecomposedFixedPointVector', 714
  `DecomposeTensorProduct', 658
  `Decomposition', 245
  `DecompositionInt', 246
  `DecompositionMatrix', 744
  decomposition matrix, 245
  Decompositions, \indexit{245}
  `Decreased', 787
  `DefaultField', 579
    \sub for cyclotomics, 160
    \sub for finite field elements, 587
  `DefaultFieldByGenerators', 579
  `DefaultFieldOfMatrix', 226
  `DefaultFieldOfMatrixGroup', 430
  `DefaultRing', 562
    \sub for finite field elements, 587
  `DefaultRingByGenerators', 563
  `DefaultStabChainOptions', 423
  Defining a Pcgs Yourself, \indexit{437}
  `DefiningPolynomial', 580
  `DefiningQuotientHomomorphism', 477
  `DegreeFFE', 586
  `DegreeIndeterminate', 675
  `DegreeOfBinaryRelation', 316
  `DegreeOfCharacter', 778
  `DegreeOfLaurentPolynomial', 674
  `DegreeOfTransformation', 555
  `DegreeOfTransformationSemigroup', 541
  `DegreeOverPrimeField', 580
  `Delta', 825
  denominator, of a rational, 146
  `DenominatorCyc', 160
  `DenominatorOfModuloPcgs', 443
  `DenominatorOfRationalFunction', 673
  `DenominatorRat', 146
  deprecated, 850
  `DepthOfPcElement', 439
  `DepthOfUpperTriangularMatrix', 235
  `Derangements', 151
  `Derivations', 642
  `Derivative', 676
  `DerivedLength', 371
  `DerivedSeriesOfGroup', 371
  `DerivedSubgroup', 363
  `DerivedSubgroupsTom', 713
  `DerivedSubgroupsTomPossible', 713
  `DerivedSubgroupsTomUnique', 713
  `DerivedSubgroupTom', 713
  `DescriptionOfRootOfUnity', 160
  `Determinant', 227
  determinant character, 781
  `DeterminantIntMat', 245
  `DeterminantMat', 227
  `DeterminantMatDestructive', 227
  `DeterminantMatDivFree', 227
  Determinant of an integer matrix, \indexit{245}
  `DeterminantOfCharacter', 781
  Developing rewriting systems, \indexit{348}
  `DiagonalizeIntMat', 243
  `DiagonalizeMat', 232
  `DiagonalMat', 228
  `DiagonalOfMat', 235
  `Difference', 276
  `DifferenceBlist', 212
  `DihedralGroup', 512
  `Dimension', 576
  `DimensionOfHighestWeightModule', 658
  `DimensionOfMatrixGroup', 430
  `DimensionOfVectors', 608
  `DimensionsLoewyFactors', 372
  `DimensionsMat', 226
  Directories, \indexit{91}
  `DirectoriesLibrary', 91
  `DirectoriesPackageLibrary', 848
  `DirectoriesPackagePrograms', 849
  `DirectoriesSystemPrograms', 92
  `Directory', 91
  `DirectoryContents', 92
  `DirectoryCurrent', 91
  `DirectoryTemporary', 91
  `DirectProduct', 505
  `DirectProductOp', 505
  Direct Products, \indexit{505}
  `DirectSumDecomposition', 627
    \sub for Lie algebras, 646
  Direct Sum Decompositions, \indexit{646}
  `DirectSumOfAlgebraModules', 638
    \sub for Lie algebras, 661
  `DirectSumOfAlgebras', 626
  `DisableAttributeValueStoring', 123
  disable automatic loading, 846
  `Discriminant', 676
  `Display', 67
    \sub for character tables, 748, 775
    \sub for tables of marks, 706
  `DisplayCacheStats', 84
  `DisplayCompositionSeries', 370
  `DisplayEggBoxOfDClass', 543
  `DisplayImfInvariants', 532
  `DisplayInformationPerfectGroups', 525
  `DisplayOptions', 750
  `DisplayOptionsStack', 89
  `DisplayProfile', 83
  `DisplayRevision', 84
  `DistancesDistributionMatFFEVecFFE', 220
  `DistancesDistributionVecFFEsVecFFE', 220
  `DistanceVecFFE', 220
  Distinguished Subalgebras, \indexit{643}
  division, 48
    \sub operation, 297
  `DivisionRingByGenerators', 579
  division rings, 578
  divisors, of an integer, 134
  `DivisorsInt', 134
  Dixon-Schneider algorithm, 754
  `DixonInit', 755
  `DixonRecord', 755
  `DixonSplit', 755
  `DixontinI', 755
  `DMYDay', 260
  `DMYhmsSeconds', 261
  `DnLattice', 788
  `DnLatticeIterative', 789
  `do', 53
  document formats (text, dvi, ps, pdf, html), 23
  `Domain', 293
  `DomainByGenerators', 293
  Domain Categories, \indexit{290}
  Domains, \indexit{110}
  Domains Generated by Class Functions, \indexit{801}
  Domains of Subspaces of Vector Spaces, \indexit{601}
  `DominantCharacter', 657
  `DominantWeights', 657
  `DoubleCoset', 359
  `DoubleCosetRepsAndSizes', 360
  Double Cosets, \indexit{359}
  `DoubleCosets', operation, 359
  `DoubleCosetsNC', operation, 359
  doublequote character, 252
  doublequotes, 250
  `DownEnv', 71
  Dummy Streams, \indexit{106}
  duplicate free, 195
  `DuplicateFreeList', 200
  Duplication of Lists, \indexit{181}
  Duplication of Objects, \indexit{113}
  `DxIncludeIrreducibles', 755
\letter E
  `E', 157
  $e_N$, 161
  `EANormalSeriesByPcgs', 445
  `Earns', 407
  `EB', 161
  `EC', 161
  Echelonized Matrices, \indexit{232}
  `ED', 161
  `Edit', 75
  Editing Files, \indexit{75}
  Editor Support, \indexit{75}
  `EE', 161
  `EF', 161
  Efficiency of Homomorphisms, \indexit{388}
  `EG', 161
  `EggBoxOfDClass', 543
  `EH', 161
  `EI', 162
  `Eigenspaces', 231
  `Eigenvalues', 231
  `EigenvaluesChar', 781
  `Eigenvectors', 231
  Eigenvectors and eigenvalues, \indexit{231}
  `EJ', 162
  `EK', 162
  `EL', 162
  `ElementaryAbelianGroup', 512
  `ElementaryAbelianSeries', 371
  `ElementaryAbelianSeriesLargeSteps', 371
  Elementary Divisors, \indexit{232}
  `ElementaryDivisorsMat', 232
  `ElementaryDivisorsMatDestructive', 232
  Elementary Operations for a Pcgs, \indexit{438}
  Elementary Operations for a Pcgs and an Element, \indexit{439}
  Elementary Operations for Integers, \indexit{127}
  Elementary Operations for Rationals, \indexit{145}
  Elementary Tietze Transformations, \indexit{493}
  `ElementOfFpGroup', 466
  `ElementOfFpSemigroup', 552
  `ElementOfMagmaRing', 665
  `ElementOrdersPowerMap', 804
  `ElementProperty', 427
  `Elements', 273
  elements, definition, 109
    \sub of a list or collection, 273
  Elements as equivalence classes, \indexit{109}
  `ElementsFamily', 268
  Elements in Algebraic Extensions, \indexit{692}
  Elements of Free Magma Rings, \indexit{665}
  Elements of pc groups, \indexit{454}
  `ElementsStabChain', 425
  Elements with Prescribed Images, \indexit{403}
  element test, for lists, 183
  `elif', 51
  `EliminatedWord', 336
  `EliminationOrdering', 685
  `else', 51
  `EM', 162
  `emacs', 75
  `Embedding', 306
    \sub example for direct products, 505
    \sub example for semidirect products, 507
    \sub example for wreath products, 508
    \sub for group products, 510
    \sub for Lie algebras, 641
    \sub for magma rings, 665
  embeddings, find all, 394
  Embeddings and Projections for Group Products, \indexit{510}
  `EmptyBinaryRelation', 315
  `EmptyMatrix', 228
  `EmptyPlist', 183
  `EmptySCTable', 617
  `EmptyStabChain', 426
  `EmptyString', 253
  `EnableAttributeValueStoring', 123
  `End', 611
  `end', 55
  Enlarging Internally Represented Lists, \indexit{183}
  `Enumerator', 269
  `EnumeratorByBasis', 604
  `EnumeratorByFunctions', 270
  Enumerators, \indexit{209}
  `EnumeratorSorted', 269
  environment, 55
  `Epicentre', 383
  `EpimorphismFromFreeGroup', 354
  `EpimorphismNilpotentQuotient', 478
  `EpimorphismNonabelianExteriorSquare', 383
  `EpimorphismPGroup', 478
  `EpimorphismQuotientSystem', 478
  epimorphisms, find all, 394
  `EpimorphismSchurCover', 383
  equality, associative words, 334
    \sub elements of finitely presented groups, 465
    \sub nonassociative words, 328
    \sub of records, 265
    \sub operation, 296
    \sub pcwords, 454
  Equality and Comparison of Domains, \indexit{288}
  equality test, 47
    \sub for permutations, 413
  equivalence class, 319
  Equivalence Classes, \indexit{319}
  `EquivalenceClasses', attribute, 319
  `EquivalenceClassOfElement', 319
  `EquivalenceClassOfElementNC', 319
  `EquivalenceClassRelation', 319
  equivalence relation, 316, 318
  `EquivalenceRelationByPairs', 318
  `EquivalenceRelationByPairsNC', 318
  `EquivalenceRelationByPartition', 318
  `EquivalenceRelationByPartitionNC', 318
  `EquivalenceRelationByProperty', 318
  `EquivalenceRelationByRelation', 318
  `EquivalenceRelationPartition', 318
  Equivalence Relations, \indexit{318}
  `ER', 162
  `Error', 73
  Error, \indexit{73}
  `ErrorCount', 73
  ErrorCount, \indexit{73}
  `ErrorNoTraceBack', 69
  errors, syntax, 64
  `ES', 162
  escaped characters, 252
  escaping non-special characters, 252
  `ET', 162
  `EU', 162
  `EuclideanDegree', 570
  `EuclideanQuotient', 570
  `EuclideanRemainder', 571
  Euclidean Rings, \indexit{570}
  Euler's totient function, 138
  `EulerianFunction', 369
  `EulerianFunctionByTom', 715
  `EV', 162
  `EvalStraightLineProgElm', 344
  `EvalString', 259
  evaluation, 42
    \sub strings, 258
  `EW', 162
  `EX', 162
  `ExactSizeConsiderFunction', 379
  `Exec', 108
  Exec, \indexit{108}
  execution, 49
  exit, 73
  expanded form of monomials, 689
  Expert Windows installation, \indexit{844}
  `Exponent', 369
    \sub for character tables, 736
  exponent, of the prime residue group, 139
  exponentiation, operation, 297
  `ExponentOfPcElement', 439
  `ExponentsConjugateLayer', 440
  `ExponentsOfCommutator', 440
  `ExponentsOfConjugate', 440
  `ExponentsOfPcElement', 439
  `ExponentsOfRelativePower', 440
  Exponents of Special Products, \indexit{440}
  `ExponentSumWord', 335
  `ExponentSyllable', 337
  Expressing Group Elements as Words in Generators, \indexit{354}
  Expressions, \indexit{42}
  `ExtendedPcgs', 442
  `ExtendStabChain', 426
  `Extension', 459
  `ExtensionNC', 459
  `ExtensionRepresentatives', 460
  `Extensions', 459
  Extensions of the p-adic Numbers, \indexit{695}
  `ExteriorCentre', 383
  `ExteriorPowerOfAlgebraModule', 661
  `ExternalOrbit', 410
  `ExternalOrbits', 410
  `ExternalOrbitsStabilizers', 410
  External Representation for Nonassociative Words, \indexit{330}
  external representation of polynomials, 689
  `ExternalSet', 409
  External Sets, \indexit{409}
  `ExternalSubset', 410
  `Extract', 785
  `ExtraspecialGroup', 512
  `ExtRepDenominatorRatFun', 689
  `ExtRepNumeratorRatFun', 689
  `ExtRepOfObj', external representation, for cyclotomics, 160
  `ExtRepPolynomialRatFun', 689
  `EY', 162
\letter F
  $f_N$, 161
  `FactorCosetAction', 405
    \sub for fp groups, 468
  `FactorCosetOperation', 468
  `FactorFreeSemigroupByRelations', 550
  `FactorGroup', 373
  `FactorGroupFpGroupByRels', 464
  `FactorGroupNC', 373
  `FactorGroupNormalSubgroupClasses', 766
  Factor Groups, \indexit{373}
  Factor Groups of Polycyclic Groups - Modulo Pcgs, \indexit{443}
  Factor Groups of Polycyclic Groups in their Own Representation, \indexit{444}
  `FactorGroupTom', 715
  `Factorial', 147
  `Factorization', 355
  factorization, 354
  `Factors', 570
    \sub of univariate polynomial, 678
  `FactorsInt', 132
  `FactorsOfDirectProduct', 759
  `FactorsSquarefree', 678
  Fail, \indexit{170}
  `fail', 170
  `FaithfulModule', 637
    \sub for Lie algebras, 655
  Families, \indexit{116}
  `FamiliesOfGeneralMappingsAndRanges', 314
  `FamiliesOfRows', 765
  `FamilyForOrdering', 282
  `FamilyObj', 116
  `FamilyPcgs', 454
  `FamilyRange', 314
  `FamilySource', 314
  FAQ, 837
  features, under UNIX, 27
  `fi', 51
  `Fibonacci', 155
  Fibonacci and Lucas Sequences, \indexit{155}
  `Field', 578
  `FieldExtension', 580
  field homomorphisms, Frobenius, 589
  `FieldOfMatrixGroup', 430
  `FieldOverItselfByGenerators', 580
  fields, 578
  File Access, \indexit{93}
  `FileDescriptorOfStream', 98
  `Filename', 92
  Filename, \indexit{92}
  File Operations, \indexit{94}
  File Streams, \indexit{103}
  `Filtered', 203
  Filters, \indexit{117}
  Filters Controlling the Arithmetic Behaviour of Lists, \indexit{185}
  Finding Positions in Lists, \indexit{191}
  Finding Submodules, \indexit{698}
  `FindSl2', 653
  Finish Installation and Cleanup, \indexit{835}
  Finite Field Elements, \indexit{584}
  Finitely Presented Lie Algebras, \indexit{653}
  Finitely presented monoids, \indexit{552}
  finiteness test, for a list or collection, 273
  Finite Perfect Groups, \indexit{523}
  `First', 204
  `FittingSubgroup', 364
  `Flat', 200
  flush character, 252
  For, \indexit{53}
  `ForAll', 204
  `ForAny', 204
  `for' loop, 53
  `FpElmComparisonMethod', 465
  `FpGroupPresentation', 483
  `FpGrpMonSmgOfFpGrpMonSmgElement', 550
  `FpLieAlgebraByCartanMatrix', 654
  frame, 790, 791
  `FrattiniSubgroup', 364
    \sub for groups with pcgs, 451
  `FreeAlgebra', 616
  `FreeAlgebraWithOne', 616
  `FreeAssociativeAlgebra', 616
  `FreeAssociativeAlgebraWithOne', 616
  `FreeGeneratorsOfFpGroup', 465
  `FreeGeneratorsOfFpSemigroup', 551
  `FreeGeneratorsOfWholeGroup', 465
  `FreeGroup', 332
  `FreeGroupOfFpGroup', 465
  Free Groups, Monoids and Semigroups, \indexit{332}
  `FreeLeftModule', 576
  `FreeLieAlgebra', 642
  `FreeMagma', 329
  `FreeMagmaRing', 664
  Free Magma Rings, \indexit{664}
  Free Magmas, \indexit{329}
  `FreeMagmaWithOne', 329
  Free Modules, \indexit{576}
  `FreeMonoid', 547
    \sub with example, 332
  `FreeMonoidOfRewritingSystem', 554
  `FreeProduct', 510
  Free Products, \indexit{510}
  `FreeSemigroup', 332
    \sub with examples, 540
  `FreeSemigroupOfFpSemigroup', 551
  `FreeSemigroupOfRewritingSystem', 554
  Frobenius automorphism, 589
  `FrobeniusAutomorphism', 589
  FrobeniusAutomorphism, \indexit{589}
  `FrobeniusCharacterValue', 800
  `FullMatrixAlgebra', 619
  `FullMatrixAlgebraCentralizer', 627
  `FullMatrixLieAlgebra', 642
  `FullMatrixModule', 577
  `FullMatrixSpace', 608
  `FullRowModule', 577
  `FullRowSpace', 608
  `FullTransformationSemigroup', 541
  Function, \indexit{55}
  `function', 55
  `FunctionAction', 409
  function call, 46
    \sub with arguments, 46
    \sub with options, 47
  Function Calls, \indexit{46}
  `FunctionOperation', 850
  functions, 61, 304
    \sub definition by arrow notation, 57
    \sub definition of, 55
    \sub recursive, 55
    \sub with a variable number of arguments, 46, 56
  `FunctionsFamily', 63
  Functions for Coding Theory, \indexit{220}
  Functions for GAP Packages, \indexit{847}
  Functions that do nothing, \indexit{63}
  Function that Modify Boolean Lists, \indexit{213}
  Function Types, \indexit{63}
  `FusionCharTableTom', 721
  `FusionConjugacyClasses', 807
  `FusionConjugacyClassesOp', 807
  fusions, 806
  `FusionsAllowedByRestrictions', 822
  `FusionsTom', 710
\letter G
  $G$-sets, 397, 409
  $g_N$, 161
  `gac', 35
  Galois Action, \indexit{580}
  Galois Conjugacy of Cyclotomics, \indexit{164}
  `GaloisCyc', 164
    \sub for class functions, 774
  `GaloisField', 588
  `GaloisGroup', of field, 581
    \sub of rational class of a group, 362
  Galois Groups of Abelian Number Fields, \indexit{597}
  `GaloisMat', 165
  `GaloisStabilizer', 594
  `GaloisType', 679
  `gap.rc', 32, 33
  GAP3, 34
  `Gap3CatalogueIdGroup', 521
  GAP for Macintosh OS X, \indexit{841}
  GAP for MacOS, \indexit{842}
  `GAPInfo', 851
  `GAPInfo.RootPaths', 29
  `GapInputPcGroup', 458
  `GapInputSCTable', 617
  `GAPKB_REW', 553
  GAP Root Directory, \indexit{90}
  `GasmanLimits', 87
  `GasmanMessageStatus', 87
  `GasmanStatistics', 87
  Gaussian algorithm, 230
  `GaussianIntegers', 598
  `GaussianRationals', 593
  Gaussians, \indexit{598}
  `Gcd', 571
  Gcd and Lcm, \indexit{571}
  `Gcdex', 130
  `GcdInt', 129
  `GcdOp', 571
  `GcdRepresentation', 571
  `GcdRepresentationOp', 572
  General Binary Relations, \indexit{315}
  `GeneralisedEigenspaces', 231
  `GeneralisedEigenvalues', 231
  generalized characters, 768
  `GeneralizedEigenspaces', 231
  `GeneralizedEigenvalues', 231
  `GeneralLinearGroup', 514
  `GeneralMappingByElements', 305
  General Mappings, \indexit{313}
  `GeneralMappingsFamily', 314
  `GeneralOrthogonalGroup', 515
  `GeneralUnitaryGroup', 514
  Generating Fields, \indexit{578}
  Generating modules, \indexit{574}
  Generating Rings, \indexit{562}
  generator, of the prime residue group, 140
  `GeneratorsOfAdditiveGroup', 560
  `GeneratorsOfAdditiveMagma', 560
  `GeneratorsOfAdditiveMagmaWithZero', 560
  `GeneratorsOfAlgebra', 623
  `GeneratorsOfAlgebraModule', 634
  `GeneratorsOfAlgebraWithOne', 623
  `GeneratorsOfDivisionRing', 579
  `GeneratorsOfDomain', 293
  `Generators\-Of\-Equivalence\-Relation\-Partition', 318
  `GeneratorsOfField', 579
  `GeneratorsOfGroup', 351
  `GeneratorsOfIdeal', 565
  `GeneratorsOfLeftIdeal', 566
  `GeneratorsOfLeftModule', 574
  `GeneratorsOfLeftOperatorAdditiveGroup', 574
  `GeneratorsOfLeftVectorSpace', 600
  `GeneratorsOfMagma', 323
  `GeneratorsOfMagmaWithInverses', 323
  `GeneratorsOfMagmaWithOne', 323
  `GeneratorsOfMonoid', 546
  `GeneratorsOfNearAdditiveGroup', 560
  `GeneratorsOfNearAdditiveMagma', 560
  `GeneratorsOfNearAdditiveMagmaWithZero', 560
  `GeneratorsOfPresentation', 482
  `GeneratorsOfRightIdeal', 566
  `GeneratorsOfRightModule', 575
  `GeneratorsOfRightOperatorAdditiveGroup', 575
  `GeneratorsOfRing', 563
  `GeneratorsOfRingWithOne', 567
  `GeneratorsOfRws', 346
  `GeneratorsOfSemigroup', 540
  `GeneratorsOf<Struct>', 289
  `GeneratorsOfTwoSidedIdeal', 565
  `GeneratorsOfVectorSpace', 600
  `GeneratorsPrimeResidues', 139
  `GeneratorsSmallest', 380
  `GeneratorsSubgroupsTom', 719
  `GeneratorSyllable', 337
  Generic Construction of Tables of Marks, \indexit{723}
  `GetFusionMap', 808
  Get the Archives, \indexit{832}
  getting help, 22
  `GF', 588
  `GL', 514
  GL and SL, \indexit{431}
  Global Memory Information, \indexit{87}
  `GlobalMersenneTwister', 136
  `GlobalRandomSource', 136
  `GModuleByMats', 697
  `GO', 515
  `GQuotients', 394
  `Grading', 628
  Green's Relations, \indexit{542}
  `GreensDClasses', 544
  `GreensDClassOfElement', 543
  `GreensDRelation', 543
  `GreensHClasses', 544
  `GreensHClassOfElement', 543
  `GreensHRelation', 543
  `GreensJClasses', 544
  `GreensJClassOfElement', 543
  `GreensJRelation', 543
  `GreensLClasses', 544
  `GreensLClassOfElement', 543
  `GreensLRelation', 543
  `GreensRClasses', 544
  `GreensRClassOfElement', 543
  `GreensRRelation', 543
  Groebner Bases, \indexit{686}
  `GroebnerBasis', 686
  `GroebnerBasisNC', 686
  `Group', 350
  group actions, 397, 398
    \sub operations syntax, 397
  Group Actions - Name Changes, \indexit{850}
  group algebra, 663
  Group Automorphisms, \indexit{390}
  `GroupByRws', 456
  `GroupByRwsNC', 456
  group characters, 768
  Group Elements, \indexit{350}
  `GroupGeneralMappingByImages', 386
  `GroupHClassOfGreensDClass', 544
  `GroupHomomorphismByFunction', 386
  `GroupHomomorphismByImages', 385
  `GroupHomomorphismByImagesNC', 385
  `GroupOfPcgs', 438
  group operations, 398, 850
  Group Properties, \indexit{367}
  `GroupRing', 664
  group ring, 663
  Groups of Automorphisms, \indexit{392}
  `GroupStabChain', 425
  `GroupWithGenerators', 351
  `GU', 514
\letter H
  $h_N$, 161
  `HallSubgroup', 365
  `HallSystem', 366
    \sub for groups with pcgs, 451
  Handling of Streams in the Background, \indexit{106}
  `HasAbelianFactorGroup', 373
  `HasElementaryAbelianFactorGroup', 373
  `HasIndeterminateName', 670
  `HasParent', 291
  `HasseDiagramBinaryRelation', 317
  `HeadPcElementByNumber', 440
  `HenselBound', 679
  hermite normal form, 851
  `HermiteNormalFormIntegerMat', 243
  `HermiteNormalFormIntegerMatTransform', 243
  `HeuristicCancelPolynomials', 691
  `HexStringInt', 255
  `HighestWeightModule', 660
  History of Character Theory Stuff in GAP, \indexit{726}
  `HMSMSec', 260
  `Hom', 611
  `HomeEnumerator', 409
  Homomorphism for very large groups, \indexit{389}
  `HomomorphismQuotientSemigroup', 542
  homomorphisms, find all, 394
  homomorphisms, Frobenius, field, 589
  Homomorphisms of Algebras, \indexit{629}
  `HomomorphismTransformationSemigroup', 541
  How to Implement New Kinds of Vector Spaces, \indexit{613}
  `HumanReadableDefinition', 717
\letter I
  $i_N$, 162
  `Ideal', 564
  `IdealByGenerators', 565
  `IdealNC', 565
  Ideals, \indexit{621}
  Ideals in Rings, \indexit{564}
  Ideals of semigroups, \indexit{541}
  `Idempotents', 324
  `IdempotentsTom', 710
  `IdempotentsTomInfo', 710
  Identical Lists, \indexit{180}
  Identical Objects, \indexit{110}
  Identical Records, \indexit{264}
  `IdentificationOfConjugacyClasses', 732
  `Identifier', for character tables, 739
    \sub for tables of marks, 711
  Identifiers, \indexit{42}
  `Identity', 293
  `IdentityBinaryRelation', 315
  `IdentityFromSCTable', 618
  `IdentityMapping', 306
  `IdentityMat', 228
  `IdentityTransformation', 555
  `IdFunc', 63
  `IdGap3SolvableGroup', 521
  `IdGroup', 521
  `IdSmallGroup', 521
  `IdsOfAllSmallGroups', 521
  If, \indexit{51}
  `if' statement, 51
  If Things Go Wrong, \indexit{837}
  `Image', 308
    \sub for Frobenius automorphisms, 589
  image, vector under matrix, 225
  `ImageElm', 308
  `ImageListOfTransformation', 556
  `Images', 308
  `ImagesElm', 307
  `ImageSetOfTransformation', 556
  `ImagesRepresentative', 307
  `ImagesSet', 307
  `ImagesSmallestGenerators', 389
  `ImagesSource', 307
  Images under Mappings, \indexit{307}
  `ImaginaryPart', 164
  `ImfInvariants', 534
  `ImfMatrixGroup', 535
  `ImfNumberQClasses', 532
  `ImfNumberQQClasses', 532
  `ImfNumberZClasses', 532
  `Immutable', 112
  `ImmutableBasis', 607
  `ImmutableMatrix', 237
  `in', for collections, 277
    \sub for lists, 183
    \sub for strictly sorted lists, 197
    \sub operation for, 277
  `IndependentGeneratorsOfAbelianGroup', 380
  `Indeterminate', 669
  `IndeterminateName', 670
  `Indeterminateness', 816
  `IndeterminateNumberOfLaurentPolynomial', 680
  `Indeterminate\-Number\-Of\-Univariate\-Rational\-Function', 670
  `Indeterminate\-Of\-Univariate\-Rational\-Function', 670
  Indeterminates, \indexit{669}
  `IndeterminatesOfPolynomialRing', 681
  `Index', 352
  `IndexInWholeGroup', 352
  `IndexNC', 352
  Index numbers of primitive groups, \indexit{529}
  `Indicator', 746
  `IndicatorOp', 746
  `IndicesCentralNormalSteps', 445
  `IndicesChiefNormalSteps', 446
  `IndicesEANormalSteps', 445
  `IndicesInvolutaryGenerators', 470
  `IndicesNormalSteps', 447
  `IndicesOfAdjointBasis', 624
  `IndicesPCentralNormalStepsPGroup', 446
  `IndicesStabChain', 425
  `Indirected', 812
  Induced Actions, \indexit{699}
  `InducedAutomorphism', 393
  `InducedClassFunction', 782
  `InducedClassFunctions', 783
  `InducedClassFunctionsByFusionMap', 783
  `InducedCyclic', 783
  `InducedPcgs', 441
  `InducedPcgsByGenerators', 441
  `InducedPcgsByGeneratorsNC', 441
  `InducedPcgsByPcSequence', 441
  `InducedPcgsByPcSequenceAndGenerators', 442
  `InducedPcgsByPcSequenceNC', 441
  `InducedPcgsWrtFamilyPcgs', 454
  `InducedPcgsWrtSpecialPcgs', 449
  `Inequalities', 799
  inequality, of records, 265
  inequality test, 47
  `InertiaSubgroup', 780
  Infinity, \indexit{160}
  `infinity', 160
  inflated class functions, 782
  `Info', 80
  `InfoAlgebra', 615
  `InfoAttributes', 123
  `InfoBckt', 427
  `InfoCharacterTable', 731
  `InfoCoh', 382
  `InfoComplement', 363
  `InfoCoset', 360
  `InfoFpGroup', 464
  Info Functions, \indexit{80}
  `InfoGroebner', 687
  `InfoGroup', 351
  `InfoLattice', 377
  `InfoLevel', 80
  `InfoMatrix', 223
  `InfoMonomial', 824
  `InfoNumtheor', 138
  `InfoOptions', 89
  `InfoPcSubgroup', 380
  Information about a function, \indexit{61}
  Information about the version used, \indexit{84}
  `InfoText', 739
  `InfoTom', 708
  `InfoWarning', 81
  `Init', 136
  `InitFusion', 821
  `InitPowerMap', 819
  `InjectionZeroMagma', 322
  `InnerAutomorphism', 391
  `InnerAutomorphismNC', 391
  `InnerAutomorphismsAutomorphismGroup', 392
  inner product, of group characters, 778
  Input-Output Streams, \indexit{104}
  `InputLogTo', 95
    \sub for streams, 102
    \sub stop logging input, 95
  `InputOutputLocalProcess', 105
  `InputTextFile', 103
  `InputTextNone', 106
  `InputTextString', 104
  `InputTextUser', 103
  `InsertTrivialStabilizer', 426
  `InstallAtExit', 73
  installation, 831
  Installation of GAP for MacOS, \indexit{842}
  Installation Overview, \indexit{831}
  `InstallCharReadHookFunc', 106
  `InstalledPackageVersion', 848
  `InstallFactorMaintenance', 299
  `InstallHandlingByNiceBasis', 613
  Installing a GAP Package, \indexit{846}
  `InstallIsomorphismMaintenance', 299
  `InstallSubsetMaintenance', 299
  `Int', 127
    \sub for cyclotomics, 158
    \sub for strings, 258
  `INT_CHAR', 258
  integer part of a quotient, 129
  `Integers', 126
  Integral Bases of Abelian Number Fields, \indexit{595}
  `IntegralizedMat', 246
  `IntegratedStraightLineProgram', 342
  `IntermediateGroup', 372
  `IntermediateResultOfSLP', 343
  `IntermediateResultOfSLPWithoutOverwrite', 343
  `Intermediate\-Results\-Of\-SLPWithout\-Overwrite', 343
  `IntermediateSubgroups', 372
  Internally Represented Cyclotomics, \indexit{166}
  Internally Represented Strings, \indexit{253}
  `InterpolatedPolynomial', 573
  `IntersectBlist', 213
  `Intersection', 275
    \sub for groups with pcgs, 451
  intersection, of collections, 275
    \sub of sets, 198
  `Intersection2', 275
  `IntersectionBlist', 212
  `IntersectionsTom', 715
  `IntersectSet', 198
  `IntFFE', 587
  `IntFFESymm', 587
  `IntHexString', 258
  `IntScalarProducts', 816, 817
  `IntVecFFE', 587
  `InvariantBilinearForm', 432
  `InvariantElementaryAbelianSeries', 371
  Invariant Forms, \indexit{432}, \indexit{700}
  `InvariantLattice', 434
  `InvariantQuadraticForm', 432
  `InvariantSesquilinearForm', 432
  `Invariant\-Subgroups\-Elementary\-Abelian\-Group', 378
  `Inverse', 295
  inverse, group homomorphism, 387
    \sub matrix, 225
    \sub of class function, 773
  `InverseAttr', 295
  `InverseClasses', 739
  `InverseGeneralMapping', 305
  `InverseImmutable', 295
  `InverseMap', 812
  `InverseMatMod', 239
  `InverseMutable', 295
  `InverseOp', 295
  `InverseRepresentative', 425
  `InverseSameMutability', 295
  `InverseSM', 295
  Invoking the Help, \indexit{22}
  `Irr', 735
  irrationalities, 157
  `IrrBaumClausen', 752
  `IrrConlon', 752
  `IrrDixonSchneider', 752
  Irreducibility Tests, \indexit{698}
  irreducible character, 777
  irreducible characters, computation, 755
  `IrreducibleDifferences', 784
  Irreducible Maximal Finite Integral Matrix Groups, \indexit{531}
  `IrreducibleModules', 754
    \sub for groups with pcgs, 451
  `IrreducibleRepresentations', 752
  `IrreducibleRepresentationsDixon', 753
  `IrreducibleSolvableGroup', 530
  `IrreducibleSolvableGroupMS', 530
  Irreducible Solvable Matrix Groups, \indexit{530}
  `Is16BitsFamily', 338
  `Is32BitsFamily', 338
  `Is8BitsFamily', 338
  `IsAbelian', 324
    \sub for character tables, 736
  `IsAbelianNumberField', 594
  `IsAbelianNumberFieldPolynomialRing', 682
  `IsAbelianTom', 712
  `IsAdditiveElement', 300
  `IsAdditiveElementWithInverse', 300
  `IsAdditiveElementWithZero', 300
  `IsAdditiveGroup', 559
  `IsAdditiveGroupGeneralMapping', 312
  `IsAdditiveGroupHomomorphism', 312
  `IsAdditivelyCommutative', 560
  `IsAdditivelyCommutativeElement', 302
  `IsAdditivelyCommutativeElementCollColl', 302
  `Is\-Additively\-Commutative\-Element\-Collection', 302
  `IsAdditivelyCommutativeElementFamily', 302
  `IsAdditiveMagma', 558
  `IsAdditiveMagmaWithInverses', 559
  `IsAdditiveMagmaWithZero', 558
  `IsAlgebra', 622
  `IsAlgebraGeneralMapping', 313
  `IsAlgebraHomomorphism', 313
  `IsAlgebraicElement', 693
  `IsAlgebraicExtension', 692
  `IsAlgebraModuleElement', 634
  `IsAlgebraModuleElementCollection', 634
  `IsAlgebraModuleElementFamily', 634
  `IsAlgebraWithOne', 622
  `IsAlgebraWithOneGeneralMapping', 313
  `IsAlgebraWithOneHomomorphism', 313
  `IsAlphaChar', 254
  `IsAlternatingGroup', 418
  `IsAnticommutative', 568
  `IsAntisymmetricBinaryRelation', 316
  `IsAssociated', 569
  `IsAssociative', 324
  `IsAssociativeElement', 302
  `IsAssociativeElementCollColl', 302
  `IsAssociativeElementCollection', 302
  `IsAssocWord', 331
  `IsAssocWordWithInverse', 331
  `IsAssocWordWithOne', 331
  `IsAutomorphismGroup', 392
  `IsBasicWreathLessThanOrEqual', 334
  `IsBasicWreathProductOrdering', 286
  `IsBasis', 602
  `IsBasisByNiceBasis', 613
  `IsBasisOfAlgebraModuleElementSpace', 635
  `IsBergerCondition', 825
  `IsBijective', 307
  `IsBinaryRelation', 315
    \sub same as `IsEndoGeneralMapping', 315
  `IsBLetterAssocWordRep', 338
  `IsBLetterWordsFamily', 338
  `IsBlist', 211
  `IsBlockMatrixRep', 240
  `IsBool', 170
  `IsBound', for lists, 179
  IsBound and Unbind for Lists, \indexit{179}
  IsBound and Unbind for Records, \indexit{266}
  `IsBoundGlobal', 45
  `IsBrauerTable', 730
  `IsBravaisGroup', 434
  `IsBuiltFromAdditiveMagmaWithInverses', 347
  `IsBuiltFromGroup', 347
  `IsBuiltFromMagma', 347
  `IsBuiltFromMagmaWithInverses', 347
  `IsBuiltFromMagmaWithOne', 347
  `IsBuiltFromSemigroup', 347
  `IsCanonicalBasis', 605
  `IsCanonicalBasisFullMatrixModule', 609
  `IsCanonicalBasisFullRowModule', 609
  `IsCanonicalNiceMonomorphism', 390
  `IsCanonicalPcgs', 442
  `IsCentral', 324
  `IsCentralFactor', 383
  `IsChar', 250
  `IsCharacter', 777
  `IsCharacteristicSubgroup', 353
  `IsCharacterTable', 730
  `IsCharacterTableInProgress', 730
  `IsCharCollection', 250
  `IsCheapConwayPolynomial', 590
  `IsClassFunction', 768
  `IsClassFusionOfNormalSubgroup', 746
  `IsClosedStream', 97
  `IsCochain', 656
  `IsCochainCollection', 656
  `IsCollection', 268
  `IsCollectionFamily', 268
  `IsCommutative', 324
  `IsCommutativeElement', 302
  `IsCommutativeElementCollColl', 302
  `IsCommutativeElementCollection', 302
  `IsCompositionMappingRep', 305
  `IsConfluent', 345
    \sub for pc groups, 456
  `Is\-Conjugacy\-Class\-Subgroups\-By\-Stabilizer\-Rep', 374
  `IsConjugacyClassSubgroupsRep', 374
  `IsConjugate', 362
  `IsConjugatorAutomorphism', 391
  `IsConjugatorIsomorphism', 391
  `IsConstantRationalFunction', 674
  `IsConstantTimeAccessGeneralMapping', 313
  `IsConstantTimeAccessList', 174
  `IsContainedInSpan', 607
  `IsCopyable', 112
  `IsCyc', 158
  `IsCyclic', 367
    \sub for character tables, 736
  `IsCyclicTom', 712
  `IsCyclotomic', 158
  `IsCyclotomicField', 594
  `IsCyclotomicMatrixGroup', 433
  `IsDenseList', 173
  `IsDiagonalMat', 227
  `IsDigitChar', 254
  `IsDirectoryPath', 93
  `IsDistributive', 568
  `IsDivisionRing', 578
  `IsDomain', 292
  `IsDoneIterator', 279
  `IsDoubleCoset', 360
  `IsDuplicateFree', 195
  `IsDuplicateFreeList', 195
  `IsDxLargeGroup', 756
  `IsElementaryAbelian', 367
    \sub for character tables, 736
  `IsElementOfFpMonoid', 550
  `IsElementOfFpSemigroup', 550
  `IsElementOfFreeMagmaRing', 665
  `IsElementOfFreeMagmaRingCollection', 665
  `IsElementOfFreeMagmaRingFamily', 665
  `IsElementOfMagmaRingModuloRelations', 666
  `Is\-Element\-Of\-Magma\-Ring\-Modulo\-Relations\-Collection', 666
  `Is\-Element\-Of\-Magma\-Ring\-Modulo\-Relations\-Family', 666
  `Is\-Element\-Of\-Magma\-Ring\-Modulo\-Span\-Of\-Zero\-Family', 667
  `IsEmpty', 273
  `IsEmptyString', 253
  `IsEndOfStream', 100
  `IsEndoGeneralMapping', 313
    \sub same as `IsBinaryRelation', 315
  `IsEqualSet', 197
  `IsEquivalenceClass', 319
  `IsEquivalenceRelation', 316
  `IsEuclideanRing', 570
  `IsEvenInt', 127
  `IsExecutableFile', 93
  `IsExistingFile', 93
  `IsExtAElement', 300
  `IsExternalOrbit', 410
  `IsExternalSet', 409
  `IsExternalSubset', 410
  `IsExtLElement', 300
  `IsExtRElement', 300
  `IsFamilyPcgs', 454
  `IsFFE', 584
  `IsFFECollColl', 584
  `IsFFECollection', 584
  `IsField', 578
  `IsFieldControlledByGaloisGroup', 581
  `IsFieldHomomorphism', 313
  `IsFinite', 273
    \sub for character tables, 736
  `IsFiniteDimensional', 576
    \sub for matrix algebras, 623
  `IsFiniteFieldPolynomialRing', 682
  `IsFinitelyGeneratedGroup', 368
  `IsFiniteOrderElement', 302
  `IsFiniteOrderElementCollColl', 302
  `IsFiniteOrderElementCollection', 302
  `IsFiniteOrdersPcgs', 438
  `IsFixedStabilizer', 427
  `IsFLMLOR', 622
  `IsFLMLORWithOne', 622
  `IsFpGroup', 464
  `IsFpMonoid', 550
  `IsFpSemigroup', 550
  `IsFreeGroup', 332
  `IsFreeLeftModule', 576
  `IsFreeMagmaRing', 664
  `IsFreeMagmaRingWithOne', 664
  `IsFromFpGroupGeneralMappingByImages', 396
  `IsFromFpGroupHomomorphismByImages', 396
  `Is\-From\-Fp\-Group\-Std\-Gens\-General\-Mapping\-By\-Images', 396
  `Is\-From\-Fp\-Group\-Std\-Gens\-Homomorphism\-By\-Images', 396
  `IsFullHomModule', 612
  `IsFullMatrixModule', 577
  `IsFullRowModule', 577
  `Is\-Full\-Subgroup\-GLor\-SLRespecting\-Bilinear\-Form', 432
  `Is\-Full\-Subgroup\-GLor\-SLRespecting\-Quadratic\-Form', 433
  `Is\-Full\-Subgroup\-GLor\-SLRespecting\-Sesquilinear\-Form', 432
  `IsFullTransformationSemigroup', 541
  `IsFunction', 63
  `IsGAPRandomSource', 136
  `IsGaussianIntegers', 598
  `IsGaussianRationals', 593
  `IsGaussianSpace', 607
  `IsGaussInt', 160
  `IsGaussRat', 160
  `IsGeneralizedDomain', 292
  `IsGeneralizedRowVector', 185
  `IsGeneralLinearGroup', 431
  `IsGeneralMapping', 313
  `IsGeneralMappingFamily', 314
  `IsGeneratorsOf<Struct>', 289
  `IsGL', 431
  `IsGlobalRandomSource', 136
  `IsGreensClass', 543
  `IsGreensDClass', 543
  `IsGreensDRelation', 543
  `IsGreensHClass', 543
  `IsGreensHRelation', 543
  `IsGreensJClass', 543
  `IsGreensJRelation', 543
  `IsGreensLClass', 543
  `IsGreensLessThanOrEqual', 543
  `IsGreensLRelation', 543
  `IsGreensRClass', 543
  `IsGreensRelation', 543
  `IsGreensRRelation', 543
  `IsGroup', 351
  `IsGroupGeneralMapping', 311
  `Is\-Group\-General\-Mapping\-By\-As\-Group\-General\-Mapping\-By\-Images', 396
  `IsGroupGeneralMappingByImages', 396
  `IsGroupGeneralMappingByPcgs', 396
  `IsGroupHClass', 544
  `IsGroupHomomorphism', 311
  `IsGroupOfAutomorphisms', 392
  `IsGroupRing', 664
  `IsHandledByNiceBasis', 577
    \sub for vector spaces, 613
  `IsHandledByNiceMonomorphism', 390
  `IsHasseDiagram', 316
  `IsHomogeneousList', 174
  `IsIdempotent', 295
  `IsIdenticalObj', 110
  `IsIncomparableUnder', 282
  `IsInducedFromNormalSubgroup', 827
  `IsInducedPcgs', 441
  `IsInducedPcgsWrtSpecialPcgs', 449
  `IsInfBitsFamily', 338
  `IsInfinity', 160
  `IsInjective', 307
  `IsInnerAutomorphism', 391
  `IsInputOutputStream', 104
  `IsInputStream', 97
  `IsInputTextNone', 97
  `IsInputTextStream', 97
  `IsInt', 127
  `IsIntegerMatrixGroup', 434
  `IsIntegers', 126
  `IsIntegralBasis', 605
  `IsIntegralCyclotomic', 158
  `IsIntegralRing', 567
  `IsInternallyConsistent', 114
    \sub for character tables, 745
    \sub for tables of marks, 713
  `IsIrreducibleCharacter', 777
  `IsIrreducibleRingElement', 569
  `IsIterator', 279
  `IsJacobianElement', 302
  `IsJacobianElementCollColl', 302
  `IsJacobianElementCollection', 302
  `IsJacobianRing', 568
  `IsLaurentPolynomial', 673
  `IsLaurentPolynomialDefaultRep', 689
  `IsLDistributive', 568
  `IsLeftAlgebraModuleElement', 634
  `IsLeftAlgebraModuleElementCollection', 634
  `IsLeftIdeal', 565
  `IsLeftIdealInParent', 565
  `IsLeftModule', 574
  `IsLeftModuleGeneralMapping', 312
  `IsLeftModuleHomomorphism', 312
  `IsLeftOperatorAdditiveGroup', 574
  `IsLeftSemigroupIdeal', 541
  `IsLeftVectorSpace', 599
  `IsLessThanOrEqualUnder', 282
  `IsLessThanUnder', 282
  `IsLetterAssocWordRep', 337
  `IsLetterWordsFamily', 337
  `IsLexicographicallyLess', 201
  `IsLexOrderedFFE', 585
  `IsLieAbelian', 645
  `IsLieAlgebra', 622
  `IsLieMatrix', 224
  `IsLieNilpotent', 645
  `IsLieObject', 640
  `IsLieObjectCollection', 640
  `IsLieSolvable', 645
  `IsLinearMapping', 312
  `IsLinearMappingsModule', 612
  `IsList', 173
  `IsListDefault', 186
  `IsListOrCollection', 269
  `IsLogOrderedFFE', 585
  `IsLowerAlphaChar', 254
  `IsLowerTriangularMat', 227
  `IsMagma', 320
  `IsMagmaHomomorphism', 310
  `IsMagmaRingModuloRelations', 666
  `IsMagmaRingModuloSpanOfZero', 667
  `IsMagmaWithInverses', 320
  `IsMagmaWithInversesIfNonzero', 320
  `IsMagmaWithOne', 320
  `IsMapping', 306
  `IsMatchingSublist', 194
  `IsMatrix', 223
  `IsMatrixGroup', 430
  `IsMatrixModule', 577
  `IsMatrixSpace', 607
  `IsMersenneTwister', 136
  `IsMinimalNonmonomial', 830
  `IsModuloPcgs', 443
  `IsMonoid', 546
  `IsMonomial', for characters, 827
    \sub for character tables, 736
    \sub for groups, 827
    \sub for positive integers, 828
  `IsMonomialGroup', 367
  `IsMonomialMatrix', 227
  `IsMonomialNumber', 828
  `IsMonomialOrdering', 683
  `IsMultiplicativeElement', 300
  `IsMultiplicativeElementWithInverse', 301
  `IsMultiplicativeElementWithOne', 301
  `IsMultiplicativeElementWithZero', 301
  `IsMultiplicativeGeneralizedRowVector', 185
  `IsMultiplicativeZero', 324
  `IsMutable', 112
  `IsMutableBasis', 606
  `IsNaturalAlternatingGroup', 417
  `IsNaturalGL', 432
  `IsNaturalGLnZ', 434
  `IsNaturalSL', 432
  `IsNaturalSLnZ', 434
  `IsNaturalSymmetricGroup', 417
  `IsNearAdditiveElement', 300
  `IsNearAdditiveElementWithInverse', 300
  `IsNearAdditiveElementWithZero', 300
  `IsNearAdditiveGroup', 558
  `IsNearAdditiveMagma', 558
  `IsNearAdditiveMagmaWithInverses', 558
  `IsNearAdditiveMagmaWithZero', 558
  `IsNearlyCharacterTable', 730
  `IsNearRingElement', 301
  `IsNearRingElementWithInverse', 301
  `IsNearRingElementWithOne', 301
  `IsNegRat', 146
  `IsNilpotent', for character tables, 736
    \sub for groups with pcgs, 451
  `IsNilpotentElement', 652
  `IsNilpotentGroup', 367
  `IsNilpotentTom', 712
  `IsNonassocWord', 327
  `IsNonassocWordCollection', 327
  `IsNonassocWordWithOne', 327
  `IsNonassocWordWithOneCollection', 327
  `IsNonnegativeIntegers', 126
  `IsNonSPGeneralMapping', 314
  `IsNonTrivial', 273
  `IsNormal', 352
  `IsNormalBasis', 605
  `IsNotIdenticalObj', 111
  `IsNumberField', 594
  `IsObject', 109
  `IsOddInt', 127
  isomorphic, pc group, 457, 458
  `IsomorphicSubgroups', 394
  `IsomorphismFpAlgebra', 631
  `IsomorphismFpGroup', 473
    \sub for subgroups of fp groups, 475
  `IsomorphismFpGroupByGenerators', 473
  `IsomorphismFpGroupByGeneratorsNC', 473
  `IsomorphismFpGroupByPcgs', 455
  `IsomorphismFpSemigroup', 551
  `IsomorphismGroups', 394
  `IsomorphismMatrixAlgebra', 631
  `IsomorphismPcGroup', 458
  `IsomorphismPermGroup', 417
    \sub for Imf matrix groups, 537
  `IsomorphismPermGroupImfGroup', 538
  `IsomorphismReesMatrixSemigroup', 545
  `IsomorphismRefinedPcGroup', 457
  `Isomorphism<Rep><Struct>', 290
  isomorphisms, find all, 394
  `IsomorphismSCAlgebra', 632
  `IsomorphismSimplifiedFpGroup', 476
  `IsomorphismSpecialPcGroup', 458
  `IsomorphismTransformationSemigroup', 541
  `IsomorphismTypeInfoFiniteSimpleGroup', 368
  `IsOne', 295
  `IsOperation', 63
  `IsOrdering', 281
  `IsOrderingOnFamilyOfAssocWords', 283
  `IsOrdinaryMatrix', 223
  `IsOrdinaryTable', 730
  `IsOutputStream', 97
  `IsOutputTextNone', 98
  `IsOutputTextStream', 98
  `IsPadicExtensionNumber', 696
  `IsPadicExtensionNumberFamily', 696
  `IsParentPcgsFamilyPcgs', 454
  `IsPartialOrderBinaryRelation', 316
  `IsPcGroup', 455
  `IsPcGroupGeneralMappingByImages', 396
  `IsPcGroupHomomorphismByImages', 396
  `IsPcgs', 437
  `IsPcgsCentralSeries', 445
  `IsPcgsChiefSeries', 446
  `IsPcgsElementaryAbelianSeries', 445
  `IsPcgsPCentralSeriesPGroup', 446
  `IsPerfect', for character tables, 736
  `IsPerfectGroup', 367
  `IsPerfectTom', 712
  `IsPerm', 412
  `IsPermCollColl', 412
  `IsPermCollection', 412
  `IsPermGroup', 416
  `IsPermGroupGeneralMappingByImages', 396
  `IsPermGroupHomomorphismByImages', 396
  `IsPGroup', 368
  `IsPNilpotent', 369
  `IsPolycyclicGroup', 367
  `IsPolynomial', 673
  `IsPolynomialDefaultRep', 689
  `IsPolynomialFunction', 672
  `IsPolynomialFunctionsFamily', 687
  `IsPolynomialRing', 682
  `IsPosInt', 127
  `IsPositiveIntegers', 126
  `IsPosRat', 146
  `Is\-Preimages\-By\-As\-Group\-General\-Mapping\-By\-Images', 396
  `IsPreOrderBinaryRelation', 316
  `IsPrime', 569
  `IsPrimeField', 580
  `IsPrimeInt', 131
  `IsPrimeOrdersPcgs', 438
  `IsPrimePowerInt', 132
  `IsPrimitive', 408
  `IsPrimitiveCharacter', 826
  `IsPrimitivePolynomial', 674
  `IsPrimitiveRootMod', 140
  `IsProbablyPrimeInt', 131
  `IsPseudoCanonicalBasisFullHomModule', 612
  `IsPSolvable', 369
  `IsPSolvableCharacterTable', 746
  `IsPSolvableCharacterTableOp', 746
  `IsPurePadicNumber', 695
  `IsPurePadicNumberFamily', 695
  `IsQuasiPrimitive', 826
  `IsQuaternion', 623
  `IsQuaternionCollColl', 623
  `IsQuaternionCollection', 623
  `IsQuickPositionList', 209
  `IsQuotientSemigroup', 542
  `IsRandomSource', 136
  `IsRange', 208
  `IsRat', 145
  `IsRationalFunction', 672
  `IsRationalFunctionDefaultRep', 689
  `IsRationalFunctionsFamily', 687
  `IsRationalMatrixGroup', 433
  `IsRationals', 145
  `IsRationalsPolynomialRing', 682
  `IsRDistributive', 568
  `IsReadableFile', 93
  `IsReadOnlyGlobal', 44
  `IsRecord', 262
  `IsRecordCollColl', 262
  `IsRecordCollection', 262
  `IsReduced', 346
  `IsReductionOrdering', 283
  `IsReesCongruence', 542
  `IsReesCongruenceSemigroup', 541
  `IsReesMatrixSemigroup', 544
  `IsReesMatrixSemigroupElement', 545
  `IsReesZeroMatrixSemigroup', 544
  `IsReesZeroMatrixSemigroupElement', 545
  `IsReflexiveBinaryRelation', 315
  `IsRegular', 407
  `IsRegularDClass', 544
  `IsRegularSemigroup', 540
  `IsRegularSemigroupElement', 540
  `IsRelativelySM', 829
  `IsRestrictedLieAlgebra', 650
  `IsRewritingSystem', 345
  `IsRightAlgebraModuleElement', 634
  `IsRightAlgebraModuleElementCollection', 634
  `IsRightCoset', 358
  `IsRightIdeal', 565
  `IsRightIdealInParent', 565
  `IsRightModule', 575
  `IsRightOperatorAdditiveGroup', 574
  `IsRightSemigroupIdeal', 541
  `IsRing', 562
  `IsRingElement', 301
  `IsRingElementWithInverse', 301
  `IsRingElementWithOne', 301
  `IsRingGeneralMapping', 313
  `IsRingHomomorphism', 313
  `IsRingWithOne', 566
  `IsRingWithOneGeneralMapping', 313
  `IsRingWithOneHomomorphism', 313
  `IsRootSystem', 647
  `IsRootSystemFromLieAlgebra', 647
  `IsRowModule', 577
  `IsRowSpace', 607
  `IsRowVector', 215
  `IsScalar', 301
  `IsSemiEchelonized', 608
  `IsSemigroup', 539
  `IsSemigroupCongruence', 542
  `IsSemigroupIdeal', 541
  `IsSemiRegular', 407
  `IsSet', 195
  `IsShortLexLessThanOrEqual', 334
  `IsShortLexOrdering', 284
  `IsSimple', for character tables, 736
  `IsSimpleAlgebra', 623
  `IsSimpleGroup', 367
  `IsSimpleSemigroup', 540
  `IsSingleValued', 306
  `IsSL', 432
  `IsSolvable', for character tables, 736
  `IsSolvableGroup', 367
  `IsSolvableTom', 712
  `IsSortedList', 195
  `IsSpecialLinearGroup', 432
  `IsSpecialPcgs', 448
  `IsSPGeneralMapping', 314
  `IsSporadicSimple', for character tables, 736
  `IsSSortedList', 195
  `IsStandardGeneratorsOfGroup', 718
  `IsStraightLineProgElm', 343
  `IsStraightLineProgram', 339
  `IsStream', 97
  `IsString', 250
  `IsStringRep', 253
  `Is<Struct>', 290
  `IsSubgroup', 352
  `IsSubgroupFpGroup', 464
  `IsSubgroupOfWholeGroupByQuotientRep', 477
  `IsSubgroupSL', 432
  `IsSubmonoidFpMonoid', 549
  `IsSubnormal', 353
  `IsSubnormallyMonomial', 829
  `IsSubsemigroupFpSemigroup', 549
  `IsSubset', 275
  `IsSubsetBlist', 212
  `IsSubsetLocallyFiniteGroup', 368
  `IsSubsetSet', 198
  `IsSubspacesVectorSpace', 601
  `IsSub<struct>', 292
  `IsSupersolvable', for character tables, 736
    \sub for groups with pcgs, 451
  `IsSupersolvableGroup', 367
  `IsSurjective', 307
  `IsSyllableAssocWordRep', 338
  `IsSyllableWordsFamily', 338
  `IsSymmetricBinaryRelation', 316
  `IsSymmetricGroup', 418
  `IsTable', 174
  `IsTableOfMarks', 708
  `IsTableOfMarksWithGens', 719
  `IsToPcGroupGeneralMappingByImages', 396
  `IsToPcGroupHomomorphismByImages', 396
  `IsToPermGroupGeneralMappingByImages', 396
  `IsToPermGroupHomomorphismByImages', 396
  `IsTotal', 306
  `IsTotalOrdering', 282
  `IsTransformation', 555
  `IsTransformationCollection', 555
  `IsTransformationMonoid', 541
  `IsTransformationSemigroup', 541
  `IsTransitive', for characters, 780
    \sub for class functions, 780
    \sub for group actions, 407
  `IsTransitiveBinaryRelation', 316
  `IsTranslationInvariantOrdering', 283
  `IsTrivial', 273
  `IsTuple', 304
  `IsTwoSidedIdeal', 565
  `IsTwoSidedIdealInParent', 565
  `IsUEALatticeElement', 659
  `IsUEALatticeElementCollection', 659
  `IsUEALatticeElementFamily', 659
  `IsUniqueFactorizationRing', 567
  `IsUnit', 568
  `IsUnivariatePolynomial', 673
  `IsUnivariatePolynomialRing', 683
  `IsUnivariateRationalFunction', 673
  `IsUnknown', 168
  `IsUpperAlphaChar', 254
  `IsUpperTriangularMat', 227
  `IsValidIdentifier', 42
  `IsVector', 301
  `IsVectorSpace', 599
  `IsVirtualCharacter', 777
  `IsWeightLexOrdering', 285
  `IsWeightRepElement', 660
  `IsWeightRepElementCollection', 660
  `IsWeightRepElementFamily', 660
  `IsWellFoundedOrdering', 282
  `IsWeylGroup', 648
  `IsWholeFamily', 274
  `IsWLetterAssocWordRep', 338
  `IsWLetterWordsFamily', 338
  `IsWord', 326
  `IsWordCollection', 327
  `IsWordWithInverse', 326
  `IsWordWithOne', 326
  `IsWreathProductOrdering', 286
  `IsWritableFile', 93
  `IsZero', 295
  `IsZeroGroup', 541
  `IsZeroSimpleSemigroup', 540
  `IsZeroSquaredElement', 303
  `IsZeroSquaredElementCollColl', 303
  `IsZeroSquaredElementCollection', 303
  `IsZeroSquaredRing', 568
  `IsZmodnZObj', 135
  `IsZmodnZObjNonprime', 135
  `IsZmodpZObj', 135
  `IsZmodpZObjLarge', 135
  `IsZmodpZObjSmall', 135
  `Iterated', 206
  `Iterator', 278
  iterator, for low index subgroups, 472
  `IteratorByBasis', 604
  `IteratorByFunctions', 280
  `IteratorList', 280
  Iterators, \indexit{278}
  `IteratorSorted', 279
\letter J
  $j_N$, 162
  `Jacobi', 140
  `JenningsLieAlgebra', 651
  `JenningsSeries', 372
  `JoinEquivalenceRelations', 318
  `JoinStringsWithSeparator', 257
  `JordanDecomposition', 236
\letter K
  $k_N$, 162
  `KappaPerp', 652
  `KB_REW', 553
  `KernelOfAdditiveGeneralMapping', 312
  `KernelOfCharacter', 779
  `KernelOfMultiplicativeGeneralMapping', 311
  `KernelOfTransformation', 556
  Keywords, \indexit{41}
  `KillingMatrix', 652
  `KnownAttributesOfObject', 121
  Known Problems of the Configure Process, \indexit{838}
  `KnownPropertiesOfObject', 124
  `KnownTruePropertiesOfObject', 124
  `KnowsHowToDecompose', 384
  `KnuthBendixRewritingSystem', 554
  Krasner-Kaloujnine theorem, 509
  `KroneckerProduct', 229
  `KuKGenerators', 509
\letter L
  $l_N$, 162
  `Lambda', 138
  Language Overview, \indexit{39}
  larger or equal, 47
  larger test, 47
  `LargestElementGroup', 380
  `LargestElementStabChain', 425
  `LargestMovedPoint', 413
  `LargestUnknown', 168
  `last', 64
  `LastSystemError', 90
  `LaTeXStringDecompositionMatrix', 744
  lattice base reduction, 246, 247
  lattice basis reduction, for virtual characters, 785
  `LatticeByCyclicExtension', 377
  `LatticeGeneratorsInUEA', 659
  Lattice Reduction, \indexit{246}
  `LatticeSubgroups', 375
  `LatticeSubgroupsByTom', 706
  `LaurentPolynomialByCoefficients', 680
  `LaurentPolynomialByExtRep', 690
  `LaurentPolynomialByExtRepNC', 690
  Laurent Polynomials, \indexit{680}
  `LClassOfHClass', 543
  `Lcm', 572
  `LcmInt', 130
  `LcmOp', 572
  `LeadCoeffsIGS', 442
  `LeadingCoefficient', 675
  `LeadingCoefficientOfPolynomial', 684
  `LeadingExponentOfPcElement', 439
  `LeadingMonomial', 676
  `LeadingMonomialOfPolynomial', 683
  `LeadingTermOfPolynomial', 683
  Leaving GAP, \indexit{73}
  `LeftActingAlgebra', 635
  `LeftActingDomain', 575
  `LeftActingRingOfIdeal', 566
  `LeftAlgebraModule', 633
  `LeftAlgebraModuleByGenerators', 633
  left cosets, 358
  `LeftDerivations', 642
  `LeftIdeal', 564
  `LeftIdealByGenerators', 565
  `LeftIdealNC', 565
  `LeftModuleByGenerators', 575
  `LeftModuleByHomomorphismToMatAlg', 636
  `LeftModuleGeneralMappingByImages', 610
  `LeftModuleHomomorphismByImages', 610
  `LeftModuleHomomorphismByImagesNC', 610
  `LeftModuleHomomorphismByMatrix', 611
  `LeftQuotient', 297
    \sub for words, 335
  `LeftShiftRowVector', 219
  legacy, 850
  `Legendre', 141
  `Length', 195
    \sub of an associative word, 335
  length, of a word, 335
  `LengthsTom', 709
  `LenstraBase', 596
  `LessThanFunction', 282
  `LessThanOrEqualFunction', 282
  `LetterRepAssocWord', 338
  `LevelsOfGenerators', 286
  `LeviMalcevDecomposition', 628
    \sub for Lie algebras, 646
  Lexical Structure, \indexit{40}
  `LexicographicOrdering', 283
  `LGFirst', 449
  `LGLayers', 449
  `LGLength', 449
  `LGWeights', 448
  library tables, 727
  `LieAlgebra', 641
  `LieAlgebraByStructureConstants', 641
  `LieBracket', 297
  `LieCenter', 643
  `LieCentralizer', 643
  `LieCentre', 643
  `LieCoboundaryOperator', 656
  `LieDerivedSeries', 644
  `LieDerivedSubalgebra', 644
  `LieFamily', 641
  `LieLowerCentralSeries', 645
  `LieNilRadical', 644
  `LieNormalizer', 643
  `LieObject', 640
  Lie objects, \indexit{640}
  `LieSolvableRadical', 644
  `LieUpperCentralSeries', 645
  `LiftedInducedPcgs', 444
  `LiftedPcElement', 444
  `LinearAction', 450
  `LinearActionLayer', 450
  `LinearCharacters', 736
  `LinearCombination', 604
  `LinearCombinationPcgs', 439
  Linear equations over the integers and Integral Matrices, \indexit{241}
  `LinearIndependentColumns', 246
  Linear Mappings, \indexit{312}
  `LinearOperation', 450
  `LinearOperationLayer', 450
  Line Editing, \indexit{74}
  `LinesOfStraightLineProgram', 340
  `List', 203
  list and non-list, difference, 188
    \sub left quotient, 190
    \sub mod, 190
    \sub product, 189
    \sub quotient, 190
  List Assignment, \indexit{177}
  list assignment, operation, 175
  `ListBlist', 212
  list boundedness test, operation, 175
  List Categories, \indexit{173}
  list element, access, 175
    \sub assignment, 177
    \sub operation, 175
  List Elements, \indexit{175}
  list equal, comparison, 184
  `ListN', 206
  list of available books, 23
  `ListPerm', 415
  Lists and Collections, \indexit{269}
  list smaller, comparison, 184
  `ListStabChain', 425
  list unbind, operation, 175
  `ListWithIdenticalEntries', 191
  `ListX', 206
  `LLL', 785
  LLL algorithm, for Gram matrices, 247
    \sub for vectors, 246
    \sub for virtual characters, 785
  `LLLReducedBasis', 246
  `LLLReducedGramMat', 247
  `LoadDynamicModule', 35
  Loading a GAP Package, \indexit{846}
  loading a saved workspace, 37
  `LoadPackage', 846
  `local', 55
  logarithm, discrete, 140
    \sub of a root of unity, 160
  `LogFFE', 586
  logical, 170
  logical operations, 171
  `LogInt', 128
  `LogMod', 139
  `LogModShanks', 139
  `LogTo', 95
    \sub for streams, 101
    \sub stop logging, 95
  `LongestWeylWordPerm', 649
  loop, read eval print, 64
  loop, `for', 53
    \sub `repeat', 52
    \sub `while', 52
  loop over iterator, 54
  loop over object, 54
  loop over range, 53
  loops, leaving, 55
    \sub restarting, 55
  `LowercaseString', 255
  `LowerCentralSeriesOfGroup', 371
  Low Index Subgroups, \indexit{472}
  `LowIndexSubgroupsFpGroup', 472
  `LowIndexSubgroupsFpGroupIterator', 472
  Low Level Routines to Modify and Create Stabilizer Chains, \indexit{426}
  `Lucas', 155
\letter M
  $m_N$, 162
  Macintosh, 841, 842
  MacOS, 842
  `Magma', 321
  `MagmaByGenerators', 321
  `MagmaByMultiplicationTable', 322
  Magma Categories, \indexit{320}
  `MagmaElement', 322
  Magma Generation, \indexit{321}
  `MagmaHomomorphismByFunctionNC', 310
  Magma Homomorphisms, \indexit{310}
  `MagmaRingModuloSpanOfZero', 667
  Magma Rings modulo Relations, \indexit{666}
  Magma Rings modulo the Span of a Zero Element, \indexit{667}
  Magmas Defined by Multiplication Tables, \indexit{322}
  `MagmaWithInverses', 321
  `MagmaWithInversesByGenerators', 321
  `MagmaWithInversesByMultiplicationTable', 322
  `MagmaWithOne', 321
  `MagmaWithOneByGenerators', 321
  `MagmaWithOneByMultiplicationTable', 322
  Main Loop, \indexit{64}
  `MakeConfluent', 346
  `MakeImmutable', 112
  `MakeReadOnlyGlobal', 44
  `MakeReadWriteGlobal', 44
  Making transformation semigroups, \indexit{541}
  Manual Conventions, \indexit{20}
  map, parametrized, 811
  `MappedWord', 328
  `MappingByFunction', 305
  `MappingPermListList', 415
  Mappings that Respect Addition, \indexit{312}
  Mappings that Respect Multiplication, \indexit{311}
  Mappings which are Compatible with Algebraic Structures, \indexit{310}
  maps, 802
  `MarksTom', 709
  `MatAlgebra', 619
  `MatClassMultCoeffsCharTable', 748
  `MathieuGroup', 513
  `MatLieAlgebra', 642
  matrices, commutator, 226
  Matrices as Basis of a Row Space, \indexit{234}
  Matrices as Linear Mappings, \indexit{235}
  Matrices over Finite Fields, \indexit{237}
  Matrices Representing Linear Equations and the Gaussian Algorithm, \indexit{230}
  `MatrixAlgebra', 619
  `MatrixAutomorphisms', 763
  matrix automorphisms, 805
  `MatrixByBlockMatrix', 240
  Matrix Constructions, \indexit{228}
  Matrix Groups in Characteristic 0, \indexit{433}
  `MatrixLieAlgebra', 642
  `MatrixOfAction', 635
  matrix spaces, 607
  `MatScalarProducts', 778
  `MatTom', 711
  `MaximalAbelianQuotient', 373
  `MaximalBlocks', 408
  `MaximalNormalSubgroups', 375
  `MaximalSubgroupClassReps', 374
  `MaximalSubgroups', 374
    \sub for groups with pcgs, 451
  `MaximalSubgroupsLattice', 376
  `MaximalSubgroupsTom', 715
  `Maximum', 201
  `MaximumList', 202
  MeatAxe Modules, \indexit{697}
  `MeetEquivalenceRelations', 318
  `MeetMaps', 814
  Membership Test for Collections, \indexit{277}
  Membership Test for Lists, \indexit{183}
  `MemoryUsage', 114
  `MinimalElementCosetStabChain', 425
  `MinimalGeneratingSet', 380
    \sub for groups with pcgs, 451
  `MinimalNonmonomialGroup', 830
  Minimal Nonmonomial Groups, \indexit{830}
  `MinimalNormalSubgroups', 375
  `MinimalPolynomial', 677
    \sub over a field, 581
    \sub over a ring, 677
  Minimal Polynomials, \indexit{677}
  `MinimalStabChain', 423
  `MinimalSupergroupsLattice', 376
  `MinimalSupergroupsTom', 716
  `MinimizedBombieriNorm', 679
  `Minimum', 201
  `MinimumList', 202
  `MinusCharacter', 820
  Miscellaneous, \indexit{144}
  Miscellaneous Name Changes or Removed Names, \indexit{851}
  mod, integers, 135
    \sub laurent polynomials, 671
    \sub lists, 190
    \sub rationals, 48
  `mod', 48
    \sub arithmetic operators, 48
    \sub for character tables, 734
    \sub residue class rings, 134
  modular inverse, 48
  modular remainder, 48
  modular roots, 142
  `ModuleByRestriction', 637
  Module Constructions, \indexit{697}
  Module Homomorphisms, \indexit{700}
  `ModuleOfExtension', 460
  Modules over Lie Algebras and Their Cohomology, \indexit{655}
  Modules over Semisimple Lie Algebras, \indexit{657}
  modulo, 48
    \sub arithmetic operators, 48
    \sub for pcgs, 443
    \sub residue class rings, 134
  `ModuloPcgs', 443
  `MoebiusMu', 143
  `MoebiusTom', 711
  Molien Series, \indexit{792}
  `MolienSeries', 792
  `MolienSeriesInfo', 792
  `MolienSeriesWithGivenDenominator', 793
  `Monoid', 546
  `MonoidByGenerators', 546
  `MonoidByMultiplicationTable', 547
  `MonoidOfRewritingSystem', 554
  `MonomialComparisonFunction', 684
  `MonomialExtGrlexLess', 686
  `MonomialExtrepComparisonFun', 684
  `MonomialGrevlexOrdering', 685
  `MonomialGrlexOrdering', 685
  `MonomialLexOrdering', 684
  Monomial Orderings, \indexit{683}
  `MonomialTotalDegreeLess', 851
  monomorphisms, find all, 394
  `MorClassLoop', 394
  More about Boolean Lists, \indexit{214}
  More About Global Variables, \indexit{44}
  More about Tables of Marks, \indexit{703}
  `MostFrequentGeneratorFpGroup', 470
  `MovedPoints', 414
  Moved Points of Permutations, \indexit{413}
  `MTX.BasesCompositionSeries', 699
  `MTX.BasesMaximalSubmodules', 699
  `MTX.BasesMinimalSubmodules', 698
  `MTX.BasesMinimalSupermodules', 699
  `MTX.BasesSubmodules', 698
  `MTX.BasisInOrbit', 700
  `MTX.BasisRadical', 699
  `MTX.BasisSocle', 699
  `MTX.CollectedFactors', 699
  `MTX.CompositionFactors', 699
  `MTX.DegreeSplittingField', 698
  `MTX.Dimension', 698
  `MTX.Distinguish', 700
  `MTX.Field', 698
  `MTX.Generators', 698
  `MTX.Homomorphism', 700
  `MTX.Homomorphisms', 700
  `MTX.InducedAction', 699
  `MTX.InducedActionFactorMatrix', 699
  `MTX.InducedActionFactorModule', 699
  `MTX.InducedActionMatrix', 699
  `MTX.InducedActionMatrixNB', 699
  `MTX.InducedActionSubmodule', 699
  `MTX.InducedActionSubmoduleNB', 699
  `MTX.InvariantBilinearForm', 700
  `MTX.InvariantQuadraticForm', 700
  `MTX.InvariantSesquilinearForm', 700
  `MTX.IsAbsolutelyIrreducible', 698
  `MTX.IsEquivalent', 700
  `MTX.IsIrreducible', 698
  `MTX.Isomorphism', 700
  `MTX.NormedBasisAndBaseChange', 699
  `MTX.OrthogonalSign', 700
  `MTX.ProperSubmoduleBasis', 698
  `MTX.SubGModule', 698
  `MTX.SubmoduleGModule', 698
  multiplication, 48
    \sub matrices, 225
    \sub matrix and matrix list, 226
    \sub matrix and scalar, 224
    \sub matrix and vector, 225
    \sub operation, 297
    \sub scalar and matrix, 224
    \sub scalar and matrix list, 226
    \sub scalar and vector, 216
    \sub vector and matrix, 225
    \sub vector and matrix list, 226
    \sub vector and scalar, 216
    \sub vectors, 216
  `MultiplicationTable', 322
  Multiplicative Arithmetic for Lists, \indexit{188}
  Multiplicative Arithmetic Functions, \indexit{142}
  `MultiplicativeNeutralElement', 324
  multiplicative order of an integer, 139
  `MultiplicativeZero', 324
  `MultiplicativeZeroOp', 294
  multiplicity, of constituents of a group character, 778
  multiplier, 383
  multisets, 197
  Multivariate Polynomials, \indexit{677}
  `MultRowVector', 219
  Murnaghan components, 790, 791
  Mutability and Copyability, \indexit{111}
  Mutability Status and List Arithmetic, \indexit{190}
  Mutable Bases, \indexit{606}
  `MutableBasis', 606
  `MutableBasisOfClosureUnderAction', 625
  `Mutable\-Basis\-Of\-Ideal\-In\-Nonassociative\-Algebra', 626
  `MutableBasisOfNonassociativeAlgebra', 626
  `MutableCopyMat', 229
  `MutableIdentityMat', 229
  `MutableNullMat', 229
\letter N
  $n_k$, 163
  `Name', 114
  `NameFunction', 61
  `NameRNam', 267
  `NamesFilter', 118
  `NamesGVars', 45
  `NamesLocalVariablesFunction', 61
  `NamesOfFusionSources', 809
  `NamesSystemGVars', 45
  `NamesUserGVars', 45
  `NaturalCharacter', 776
  Natural Embeddings related to Magma Rings, \indexit{665}
  `NaturalHomomorphismByGenerators', 310
  `NaturalHomomorphismByIdeal', 631
  `NaturalHomomorphismByNormalSubgroup', 373
  `NaturalHomomorphismByNormalSubgroupNC', 373
  `NaturalHomomorphismBySubAlgebraModule', 638
  `NaturalHomomorphismBySubspace', 611
  `NearAdditiveGroup', 559
  `NearAdditiveGroupByGenerators', 559
  `NearAdditiveMagma', 559
  `NearAdditiveMagmaByGenerators', 559
  `NearAdditiveMagmaWithZero', 559
  `NearAdditiveMagmaWithZeroByGenerators', 559
  `NearlyCharacterTablesFamily', 731
  negative number, 48
  `NegativeRoots', 647
  `NegativeRootVectors', 647
  `NestingDepthA', 186
  `NestingDepthM', 186
  `NewInfoClass', 80
  newline, 41
  newline character, 252
  `NewmanInfinityCriterion', 480
  New Presentations and Presentations for Subgroups, \indexit{475}
  `NextIterator', 279
  `NextPrimeInt', 132
  `NF', 593
  `NiceBasis', 613
  `NiceBasisFiltersInfo', 614
  `NiceFreeLeftModule', 613
  `NiceFreeLeftModuleInfo', 613
  `NiceMonomorphism', 390
  `NiceMonomorphismAutomGroup', 393
  Nice Monomorphisms, \indexit{390}
  `NiceObject', 390
  `NiceVector', 613
  `NilpotencyClassOfGroup', 367
  `NilpotentQuotientOfFpLieAlgebra', 654
  `NK', 163
  `NOAUTO', 847
  `NonabelianExteriorSquare', 383
  `NonnegativeIntegers', 126
  `NonnegIntScalarProducts', 816, 817
  `NonNilpotentElement', 652
  `Norm', 581
    \sub of character, 778
  `NormalBase', 583
  `NormalClosure', 363
  `NormalFormIntMat', 244
  Normal Forms of Integer Matrices - Name Changes, \indexit{851}
  Normal Forms over the Integers, \indexit{242}
  `NormalIntersection', 363
  `Normalized\-Element\-Of\-Magma\-Ring\-Modulo\-Relations', 666
  `NormalizedWhitespace', 256
  `Normalizer', 362
  normalizer, 362
  `NormalizerInGLnZ', 434
  `NormalizerInGLnZBravaisGroup', 434
  `NormalizersTom', 713
  `NormalizerTom', 713
  `NormalizeWhitespace', 256
  `NormalSeriesByPcgs', 447
  Normal Structure, \indexit{362}
  `NormalSubgroupClasses', 766
  `NormalSubgroupClassesInfo', 765
  `NormalSubgroups', 375
  `NormedRowVector', 217
  `NormedRowVectors', 610
  `NormedVectors', 851
  `not', 172
  `NrArrangements', 150
  `NrBasisVectors', 606
  `NrCombinations', 149
  `NrConjugacyClasses', 361
    \sub for character tables, 736
  `NrConjugacyClassesGL', 517
  `NrConjugacyClassesGU', 517
  `NrConjugacyClassesPGL', 517
  `NrConjugacyClassesPGU', 517
  `NrConjugacyClassesPSL', 517
  `NrConjugacyClassesPSU', 517
  `NrConjugacyClassesSL', 517
  `NrConjugacyClassesSLIsogeneous', 517
  `NrConjugacyClassesSU', 517
  `NrConjugacyClassesSUIsogeneous', 517
  `NrDerangements', 152
  `NrInputsOfStraightLineProgram', 340
  `NrMovedPoints', 414
  `NrOrderedPartitions', 154
  `NrPartitions', 153
  `NrPartitionsSet', 152
  `NrPartitionTuples', 155
  `NrPermutationsList', 151
  `NrPolyhedralSubgroups', 747
  `NrPrimitiveGroups', 528
  `NrRestrictedPartitions', 154
  `NrSubsTom', 709
  `NrTransitiveGroups', 519
  `NrTuples', 151
  `NrUnorderedTuples', 150
  `NullAlgebra', 620
  `NullMat', 228
  `NullspaceIntMat', 241
  `NullspaceMat', 230
  `NullspaceMatDestructive', 230
  `NullspaceModQ', 239
  `Number', 203
  number, Bell, 148
    \sub binomial, 147
    \sub Stirling, of the first kind, 148
    \sub Stirling, of the second kind, 149
  `NumberArgumentsFunction', 61
  `NumberFFVector', 218
  number field, 594
  number fields, Galois group, 597
  `NumberIrreducibleSolvableGroups', 530
  `NumberPerfectGroups', 524
  `NumberPerfectLibraryGroups', 524
  `NumberSmallGroups', 521
  `NumberSyllables', 336
  numerator, of a rational, 146
  `NumeratorOfModuloPcgs', 443
  `NumeratorOfRationalFunction', 672
  `NumeratorRat', 146
  Numerical Group Attributes, \indexit{369}
\letter O
  $O_p(G)$, see `PCore', 362
  `ObjByExtRep', 659
  Objects, \indexit{109}
  obsolete, 850
  `OCOneCocycles', 382
  octal character codes, 252
  `OctaveAlgebra', 619
  `od', 53
  `OldGeneratorsOfPresentation', 498
  `Omega', 366
  `ONanScottType', 418
  `OnBreak', 68
  `OnBreakMessage', 70
  `One', 293
  `OneAttr', 293
  `OneCoboundaries', 381
  `OneCocycles', 381
  one cohomology, 380
  `OneFactorBound', 679
  `OneImmutable', 293
  `OneIrreducibleSolvableGroup', 530
  `One<Library>Group', 519
  `OneMutable', 293
  `OneOfPcgs', 438
  `OneOp', 293
  `OnePrimitiveGroup', 519
  `OneSameMutability', 293
  `OneSM', 293
  `OneSmallGroup', 521
  `OneTransitiveGroup', 519
  `OnIndeterminates', 677
    \sub as a permutation action, 399
  `OnLeftInverse', 398
  `OnLines', 399
    \sub example, 514
  `OnPairs', 398
  `OnPoints', 398
  `OnRight', 398
  `OnSets', 398
  `OnSetsDisjointSets', 399
  `OnSetsSets', 398
  `OnSetsTuples', 399
  `OnSubspacesByCanonicalBasis', 400
  `OnTuples', 398
  `OnTuplesSets', 399
  `OnTuplesTuples', 399
  `Operation', 850
  `OperationAlgebraHomomorphism', 631
  Operational Structure of Domains, \indexit{287}
  `OperationHomomorphism', 850
  operations, for booleans, 171
  Operations and Attributes for Vector Spaces, \indexit{600}
  Operations applicable to All Streams, \indexit{98}
  Operations Concerning Blocks, \indexit{742}
  Operations for (Near-)Additive Magmas, \indexit{561}
  Operations for Abelian Number Fields, \indexit{593}
  operations for algebraic elements, 692
  Operations for Associative Words, \indexit{335}
  Operations for Associative Words by their Syllables, \indexit{336}
  Operations for Booleans, \indexit{171}
  Operations for Brauer Characters, \indexit{800}
  Operations for Class Functions, \indexit{777}
  Operations for Collections, \indexit{275}
  Operations for Cyclotomics, \indexit{157}
  Operations for Domains, \indexit{292}
  Operations for Finite Field Elements, \indexit{586}
  Operations for Finitely Presented Groups, \indexit{466}
  Operations for Group Homomorphisms, \indexit{387}
  Operations for Input Streams, \indexit{98}
  Operations for Lists, \indexit{199}
  Operations for Output Streams, \indexit{101}
  Operations for Pc Groups, \indexit{458}
  Operations for Rational Functions, \indexit{671}
  Operations for Special Kinds of Bases, \indexit{605}
  Operations for Stabilizer Chains, \indexit{424}
  Operations for Vector Space Bases, \indexit{603}
  Operations for Words, \indexit{328}
  Operations on elements of the algebra, \indexit{346}
  Operations on rewriting systems, \indexit{345}
  Operations to Evaluate Strings, \indexit{258}
  Operations to Produce or Manipulate Strings, \indexit{255}
  Operations which have Special Methods for Groups with Pcgs, \indexit{451}
  operators, 42
    \sub arithmetic, 48
    \sub associativity, 49
    \sub for cyclotomics, 161
    \sub for lists, 185
    \sub precedence, 48, 49
  Operators for Character Tables, \indexit{734}
  Operators for Matrices, \indexit{224}
  Operators for Row Vectors, \indexit{215}
  Optimization and Compiler Options, \indexit{839}
  options, 27, 831
    \sub command line, filenames, 29
    \sub command line, internal, 31
  options, under UNIX, 27
  `or', 171
  `Orbit', 400
  `OrbitFusions', 810
  `OrbitLength', 401
  `OrbitLengths', 401
  `OrbitLengthsDomain', 401
  `OrbitPerms', 416
  `OrbitPowerMaps', 805
  `Orbits', operation/attribute, 401
  Orbits, \indexit{400}
  `OrbitsDomain', 401
  `OrbitsPerms', 416
  `OrbitStabChain', 425
  `OrbitStabilizer', 402
  `OrbitStabilizerAlgorithm', 402
  Orbit Stabilizer Methods for Polycyclic Groups, \indexit{451}
  `Order', 296
    \sub of a class function, 774
  order,  of a group, 350
    \sub of a list, collection or domain, 274
    \sub of the prime residue group, 138
  `OrderedPartitions', 153
  ordering, booleans, 171
    \sub of records, 266
  `OrderingByLessThanFunctionNC', 281
  `OrderingByLessThanOrEqualFunctionNC', 281
  `OrderingOfRewritingSystem', 345
  `OrderingOnGenerators', 283
  `OrderingsFamily', 281
  Orderings on families of associative words, \indexit{283}
  `OrderMod', 139
  `OrderOfRewritingSystem', 345
  `OrdersClassRepresentatives', 737
  `OrdersTom', 709
  `Ordinal', 259
  ordinary character, 777
  `OrdinaryCharacterTable', 736
  `OrthogonalComponents', 790
  Orthogonal Embeddings, \indexit{248}
  `OrthogonalEmbeddings', 248
  `OrthogonalEmbeddingsSpecialDimension', 786
  OSX, 841
  Other Filters, \indexit{125}
  Other Operations Applicable to any Object, \indexit{114}
  Other Operations for Character Tables, \indexit{745}
  Other Operations for Tables of Marks, \indexit{713}
  output, suppressing, 64
  `OutputLogTo', 95
    \sub for streams, 102
    \sub stop logging output, 95
  `OutputTextFile', 103
  `OutputTextNone', 106
  `OutputTextString', 104
  `OutputTextUser', 104
\letter P
  $p$-group, 368
  package, 846
  Package Interface - Obsolete Functions and Name Changes, \indexit{850}
  Packages, \indexit{835}
  `PadicCoefficients', 246
  `PadicExtensionNumberFamily', 695
  `PadicNumber', 695
    \sub for pure padics, 694
  `PadicValuation', 570
  `Pager', 25
  `Parametrized', 813
  Parametrized Maps, \indexit{811}
  parametrized maps, 802
  `Parent', 291
  `ParentPcgs', 441
  Parents, \indexit{291}
  `PartialFactorization', 133
  partial order, 316
  `PartialOrderByOrderingFunction', 317
  `PartialOrderOfHasseDiagram', 316
  `Partitions', 153
  partitions, improper, of an integer, 154
    \sub ordered, of an integer, 154
    \sub restricted, of an integer, 154
  `PartitionsGreatestEQ', 154
  `PartitionsGreatestLE', 154
  `PartitionsSet', 152
  `PartitionTuples', 155
  `PcElementByExponents', 439
  `PcElementByExponentsNC', 439
  `PCentralLieAlgebra', 651
  `PCentralNormalSeriesByPcgsPGroup', 446
  `PCentralSeries', 372
  `PcGroupCode', 462
  `PcGroupCodeRec', 462
  `PcGroupFpGroup', 455
  Pc groups versus fp groups, \indexit{455}
  `PcGroupWithPcgs', 457
  `Pcgs', 437
  `Pcgs_OrbitStabilizer', 451
  Pcgs and Normal Series, \indexit{445}
  `PcgsByPcSequence', 437
  `PcgsByPcSequenceNC', 437
  `PcgsCentralSeries', 445
  `PcgsChiefSeries', 446
  `PcgsElementaryAbelianSeries', 445
  `PcgsPCentralSeriesPGroup', 446
  `PClassPGroup', 369
  `PCore', 362
  `PcSeries', 438
  `PerfectGroup', 523
  perfect groups, 523
  `PerfectIdentification', 524
  `PerfectResiduum', 364
  `Perform', 201
  `Permanent', 156
  Permanent of a Matrix, \indexit{156}
  `PermBounds', 799
  `PermCharInfo', 794
  `PermCharInfoRelative', 795
  `PermChars', 796
  `PermCharsTom', 722
  `PermComb', 799
  `PermLeftQuoTransformation', 557
  `PermList', 415
  `PermListList', 201
  `Permutation', 406
  `PermutationCharacter', 777
  permutation character, 822
  permutation characters, possible, 793, 796
  `PermutationCycle', 406
  `PermutationCycleOp', 406
  `PermutationGModule', 697
  `PermutationMat', 228
  `PermutationsFamily', 412
  Permutations Induced by Elements and Cycles, \indexit{406}
  `PermutationsList', 151
  `PermutationTom', 708
  `Permuted', 202
    \sub as a permutation action, 400
    \sub for class functions, 774
  `PGL', 516
  `PGU', 516
  `Phi', 138
  point stabilizer, 402
  Polycyclic Generating Systems, \indexit{436}
  `PolynomialByExtRep', 690
  `PolynomialByExtRepNC', 690
  `PolynomialCoefficientsOfPolynomial', 675
  `PolynomialDivisionAlgorithm', 686
  Polynomial Factorization, \indexit{678}
  `PolynomialModP', 678
  `PolynomialReducedRemainder', 686
  `PolynomialReduction', 685
  `PolynomialRing', 681
  Polynomial Rings, \indexit{681}
  Polynomials as Univariate Polynomials in one Indeterminate, \indexit{675}
  polynomials over abelian number fields, factors, 593
  Polynomials over the Rationals, \indexit{678}
  `PopOptions', 88
  Portability, \indexit{90}
  Porting GAP, \indexit{840}
  `Position', 191
  `PositionBound', 193
  `PositionCanonical', 192
  `PositionFirstComponent', 194
  `PositionNonZero', 194
  `PositionNot', 194
  `PositionNthOccurrence', 192
  `PositionProperty', 193
  `Positions', 192
  `PositionSet', 193
  `PositionsOp', 192
  `PositionSorted', 192
  `PositionStream', 100
  `PositionSublist', 194
  `PositionWord', 335
  `PositiveIntegers', 126
  positive number, 48
  `PositiveRoots', 647
  `PositiveRootVectors', 647
  `PossibleClassFusions', 809
  `PossibleFusionsCharTableTom', 721
  Possible Permutation Characters, \indexit{793}
  possible permutation characters, 793, 796
  `PossiblePowerMaps', 803
  power, 48
    \sub matrix, 225
    \sub meaning for class functions, 773
    \sub of words, 335
  `PowerMap', 803
  `PowerMapByComposition', 805
  `PowerMapOp', 803
  Power Maps, \indexit{802}
  `PowerMapsAllowedBySymmetrizations', 820
  `PowerMod', 572
  `PowerModCoeffs', 221
  `PowerModInt', 131
  `PowerPartition', 155
  powerset, 149
  `PowerSubalgebraSeries', 624
  `PQuotient', 477
  precedence, 48
  precedence test, for permutations, 413
  `PrefrattiniSubgroup', 364
    \sub for groups with pcgs, 451
  `PreImage', 309
  `PreImageElm', 309
  `PreImages', 309
  `PreImagesElm', 308
  Preimages in the Free Group, \indexit{465}
  Preimages in the Free Semigroup, \indexit{551}
  `PreimagesOfTransformation', 556
  `PreImagesRange', 308
  `PreImagesRepresentative', 309
  `PreImagesSet', 309
  Preimages under Homomorphisms from an FpGroup, \indexit{476}
  Preimages under Mappings, \indexit{308}
  preorder, 316
  `PresentationFpGroup', 482
  `PresentationNormalClosure', 487
  `PresentationNormalClosureRrs', 487
  `PresentationSubgroup', 485
  `PresentationSubgroupMtc', 486
  `PresentationSubgroupRrs', 485
  `PresentationViaCosetTable', 483
  previous result, 64
  `PrevPrimeInt', 132
  `PrimaryGeneratorWords', 486
  primary subgroup generators, 500
  `PrimeBlocks', 742
  `PrimeBlocksOp', 742
  `PrimeField', 580
  Prime Integers and Factorization, \indexit{131}
  `PrimePGroup', 369
  `PrimePowersInt', 134
  prime residue group, 138
    \sub exponent, 139
    \sub generator, 140
    \sub order, 138
  Prime Residues, \indexit{138}
  `PrimeResidues', function, 138
  `Primes', 131
  primitive, 408
  `PRIMITIVE_INDICES_MAGMA', 529
  `PrimitiveElement', 580
  `PrimitiveGroup', 528
  Primitive Groups, \indexit{418}
  `PrimitiveGroupsIterator', 528
  `PrimitiveIdentification', 529
  `PrimitiveIndexIrreducibleSolvableGroup', 530
  Primitive Permutation Groups, \indexit{527}
  `PrimitivePolynomial', 678
  `PrimitiveRoot', 588
  `PrimitiveRootMod', 140
  primitive root modulo an integer, 140
  Primitive Roots and Discrete Logarithms, \indexit{139}
  Primitivity of Characters, \indexit{825}
  `Print', 66
  `PrintAmbiguity', 816
  `PrintArray', 229
  `PrintCharacterTable', 751
  `PrintFactorsInt', 134
  `PrintFormattingStatus', 102
  Printing, Viewing and Displaying Finite Field Elements, \indexit{590}
  Printing Character Tables, \indexit{748}
  Printing Class Functions, \indexit{774}
  Printing Presentations, \indexit{488}
  Printing Tables of Marks, \indexit{706}
  `PrintObj', 67
    \sub for character tables, 748, 774
    \sub for tables of marks, 706
  `PrintTo', 95
    \sub for streams, 101
  `ProbabilityShapes', 679
  problems, 837
  Problems on Particular Systems, \indexit{839}
  procedure call, 50
  Procedure Calls, \indexit{50}
  procedure call with arguments, 50
  `Process', 107
  Process, \indexit{107}
  `PROD_GF2MAT_GF2MAT_ADVANCED', 239
  `PROD_GF2MAT_GF2MAT_SIMPLE', 239
  `Product', 205
  product, of words, 335
    \sub rational functions, 671
  `ProductCoeffs', 221
  `ProductOfStraightLinePrograms', 343
  `ProductSpace', 624
  `ProductX', 207
  `ProfileFunctions', 83
  `ProfileGlobalFunctions', 83
  `ProfileMethods', 82
  `ProfileOperations', 82
  `ProfileOperationsAndMethods', 82
  `PROFILETHRESHOLD', 83
  Profiling, \indexit{82}
  `ProjectedInducedPcgs', 444
  `ProjectedPcElement', 444
  `Projection', 306
    \sub example for direct products, 505
    \sub example for semidirect products, 507
    \sub example for subdirect products, 508
    \sub example for wreath products, 508
    \sub for group products, 510
  `ProjectionMap', 812
  projections, find all, 394
  `ProjectiveActionHomomorphismMatrixGroup', 431
  `ProjectiveActionOnFullSpace', 431
  `ProjectiveGeneralLinearGroup', 516
  `ProjectiveGeneralUnitaryGroup', 516
  `ProjectiveOrder', 238
  `ProjectiveSpecialLinearGroup', 516
  `ProjectiveSpecialUnitaryGroup', 516
  `ProjectiveSymplecticGroup', 516
  prompt, 64
    \sub partial, 64
  Properties, \indexit{124}
  Properties and Attributes for Lists, \indexit{194}
  Properties and Attributes of (General) Mappings, \indexit{306}
  Properties and Attributes of Binary Relations, \indexit{315}
  Properties and Attributes of Matrices, \indexit{226}
  Properties and Attributes of Rational Functions, \indexit{672}
  Properties and basic functionality, \indexit{282}
  Properties of a Lie Algebra, \indexit{645}
  Properties of rewriting systems, \indexit{347}
  Properties of Rings, \indexit{567}
  Properties of Tables of Marks, \indexit{712}
  `PRump', 365
  `PseudoRandom', 278
  `PSL', 516
  `PSP', 516
  `PSp', 516
  `PSU', 516
  `PthPowerImage', 651
  `PthPowerImages', 651
  Pure p-adic Numbers, \indexit{694}
  `PurePadicNumberFamily', 694
  `PushOptions', 88
\letter Q
  `Quadratic', 164
  quadratic residue, 141
  `QuaternionAlgebra', 619
  `QUIET', 851
  `QUIT', emergency quit, 73
  quit, in emergency, 73
  `quit', 68
  `QUITTING', 73
  `QuoInt', 129
  `Quotient', 563
  quotient, for finitely presented groups, 464
    \sub matrices, 225
    \sub matrix and matrix list, 226
    \sub matrix and scalar, 225
    \sub of free monoid, 552
    \sub of free semigroup, 550
    \sub of words, 335
    \sub rational functions, 671
    \sub scalar and matrix, 225
    \sub scalar and matrix list, 226
    \sub vector and matrix, 225
  `QuotientFromSCTable', 618
  Quotient Methods, \indexit{477}
  `QuotientMod', 572
  `QuotientPolynomialsExtRep', 691
  `QuotientRemainder', 571
  Quotients, \indexit{542}
  Quotients and Remainders, \indexit{129}
  `QuotientSemigroupCongruence', 542
  `QuotientSemigroupHomomorphism', 542
  `QuotientSemigroupPreimage', 542
  `QuotRemLaurpols', 680
\letter R
  $r_N$, 162
  `RadicalGroup', 364
  `RadicalOfAlgebra', 627
  `Random', 136
    \sub `[coll]', 277
    \sub for integers, 129
    \sub for rationals, 146
  `RandomBinaryRelationOnPoints', 317
  random element, of a list or collection, 277
  Random Elements, \indexit{277}
  `RandomInvertibleMat', 230
  `RandomIsomorphismTest', 462
  Random Isomorphism Testing, \indexit{462}
  Randomized Methods for Permutation Groups, \indexit{420}
  `RandomList', 278
  `RandomMat', 230
  Random Matrices, \indexit{230}
  `RandomPrimitivePolynomial', 590
  random seed, 278
  `RandomSource', 137
  Random Sources, \indexit{136}
  `RandomTransformation', 555
  `RandomUnimodularMat', 230
  `Range', 307
  range, 207
  Ranges, \indexit{207}
  `RankAction', 407
  `RankFilter', 117
  `RankMat', 230
  `RankOfTransformation', 556
  `RankPGroup', 369
  `Rat', 146
    \sub for strings, 258
  `RationalClass', 361
  `RationalClasses', 362
  `RationalFunctionByExtRep', 690
  `RationalFunctionByExtRepNC', 690
  `Rational\-Function\-By\-Ext\-Rep\-With\-Cancellation', 691
  Rational Function Families, \indexit{687}
  `RationalFunctionsFamily', 687
  `RationalizedMat', 166
  `Rationals', 145
  `RClassOfHClass', 543
  `Read', 94
    \sub for streams, 99
  `ReadAll', 99
  `ReadAllLine', 105
  `ReadAsFunction', 94
    \sub for streams, 99
  `ReadByte', 99
  read eval print loop, 64
  `ReadLine', 99
  `ReadPackage', 847
  `ReadPkg', 850
  `ReadTest', 84
    \sub for streams, 99
  `RealClasses', 740
  `RealizableBrauerCharacters', 800
  `RealPart', 164
  `RecNames', 262
  Recognizing Characters, \indexit{254}
  record, component access, 263
    \sub component assignment, 263
    \sub component variable, 263
    \sub component variable assignment, 264
  Record Access Operations, \indexit{267}
  Record Assignment, \indexit{263}
  record assignment, operation, 267
  record boundness test, operation, 267
  record component, operation, 267
  record unbind, operation, 267
  Recovery from NoMethodFound-Errors, \indexit{77}
  recursion, 55
  redisplay a help section, 23
  redisplay with next help viewer, 23
  `ReduceCoeffs', 221
  `ReduceCoeffsMod', 221
  `ReducedAdditiveInverse', 346
  `ReducedCharacters', 784
  `ReducedClassFunctions', 784
  `ReducedComm', 346
  `ReducedConfluentRewritingSystem', 553
  `ReducedConjugate', 346
  `ReducedDifference', 346
  `ReducedForm', 345
  `ReducedGroebnerBasis', 687
  `ReducedInverse', 346
  `ReducedLeftQuotient', 346
  `ReducedOne', 346
  `ReducedPcElement', 439
  `ReducedPower', 346
  `ReducedProduct', 346
  `ReducedQuotient', 346
  `ReducedScalarProduct', 346
  `ReducedSum', 346
  `ReducedZero', 346
  `ReduceRules', 346
  `ReduceStabChain', 426
  Reducing Virtual Characters, \indexit{784}
  `Ree', 513
  `ReeGroup', 513
  `ReesCongruenceOfSemigroupIdeal', 541
  `ReesMatrixSemigroup', 544
  `ReesMatrixSemigroupElement', 545
  Rees Matrix Semigroups, \indexit{544}
  `ReesZeroMatrixSemigroup', 544
  `ReesZeroMatrixSemigroupElement', 545
  `ReesZeroMatrixSemigroupElementIsZero', 545
  `RefinedPcGroup', 457
  `ReflectionMat', 229
  `ReflexiveClosureBinaryRelation', 317
  reflexive relation, 315
  regular, 407
  regular action, 404
  `RegularActionHomomorphism', 405
  `RegularModule', 754
  relations, 304
  Relations Between Domains, \indexit{298}
  `RelationsOfFpSemigroup', 551
  `RelativeBasis', 603
  `RelativeBasisNC', 603
  relatively prime, 48
  `RelativeOrderOfPcElement', 439
  `RelativeOrders', of a pcgs, 438
  Relators in a Presentation, \indexit{488}
  `RelatorsOfFpGroup', 465
  remainder, operation, 297
  remainder of a quotient, 129
  `RemInt', 129
  `Remove', 178
  remove, an element from a set, 198
  `RemoveCharacters', 256
  `RemoveFile', 96
  `RemoveOuterCoeffs', 219
  `RemoveRelator', 490
  `RemoveSet', 198
  `RemoveStabChain', 426
  Repeat, \indexit{52}
  `repeat' loop, 52
  `ReplacedString', 256
  Representation, \indexit{120}
  representation, as a sum of two squares, 144
  Representations for Associative Words, \indexit{337}
  Representations for Group Homomorphisms, \indexit{396}
  Representations given by modules, \indexit{754}
  Representations of Algebras, \indexit{632}
  `RepresentationsOfObject', 121
  `Representative', 274
  representative, of a list or collection, 275
  `RepresentativeAction', 403
  `RepresentativeLinearOperation', 632
  `RepresentativeOperation', 850
  `RepresentativesContainedRightCosets', 359
  `RepresentativesFusions', 810
  `RepresentativeSmallest', 275
  `RepresentativesMinimalBlocks', 408
  `RepresentativesPerfectSubgroups', 377
  `RepresentativesPowerMaps', 805
  `RepresentativesSimpleSubgroups', 377
  `RepresentativeTom', 720
  `RepresentativeTomByGenerators', 720
  `RepresentativeTomByGeneratorsNC', 720
  `RequirePackage', 850
  `Reread', 96
  `REREADING', 96
  `RereadPackage', 847
  `RereadPkg', 850
  `Reset', 136
  `ResetOptionsStack', 88
  residue, quadratic, 141
  Residue Class Rings, \indexit{134}
  `RespectsAddition', 312
  `RespectsAdditiveInverses', 312
  `RespectsInverses', 311
  `RespectsMultiplication', 311
  `RespectsOne', 311
  `RespectsScalarMultiplication', 312
  `RespectsZero', 312
  `RestoreStateRandom', 277
  Restricted and Induced Class Functions, \indexit{782}
  `RestrictedClassFunction', 782
  `RestrictedClassFunctions', 782
  Restricted Lie algebras, \indexit{650}
  `RestrictedMapping', 306
  `RestrictedPartitions', 154
  `RestrictedPerm', 415
  `RestrictedPermNC', 415
  `RestrictedTransformation', 556
  `RestrictOutputsOfSLP', 342
  `Resultant', 676
  `ResultOfStraightLineProgram', 340
  Return, \indexit{58}
  `return', 68
    \sub no value, 58
    \sub with value, 58
  `ReturnFail', 63
  `ReturnFalse', 63
  return from break loop, 68
  `ReturnTrue', 63
  `Reversed', 200
  `RewindStream', 100
  `RewriteWord', 471
  Rewriting in Groups and Monoids, \indexit{347}
  Rewriting Systems and the Knuth-Bendix Procedure, \indexit{553}
  `RightActingAlgebra', 635
  `RightActingRingOfIdeal', 566
  `RightAlgebraModule', 633
  `RightAlgebraModuleByGenerators', 633
  `RightCoset', 357
  `RightCosets', 358
  right cosets, 357
  `RightCosetsNC', 358
  `RightDerivations', 642
  `RightIdeal', 564
  `RightIdealByGenerators', 565
  `RightIdealNC', 565
  `RightModuleByHomomorphismToMatAlg', 636
  `RightShiftRowVector', 219
  `RightTransversal', 358
  `Ring', 562
  `RingByGenerators', 563
  Ring Homomorphisms, \indexit{313}
  Rings With One, \indexit{566}
  `RingWithOne', 566
  `RingWithOneByGenerators', 567
  `RNamObj', 267
  root, of 1 modulo an integer, 142
    \sub of an integer, 128
    \sub of an integer, smallest, 128
    \sub of an integer modulo another, 141
  `RootInt', 128
  `RootMod', 141
  `RootOfDefiningPolynomial', 580
  `RootsMod', 141
  Roots Modulo Integers, \indexit{140}
  roots of unity, 157
  `RootsOfUPol', 675
  `RootsUnityMod', 142
  `RootSystem', 647
  `RoundCyc', 159
  Row and Matrix Spaces, \indexit{607}
  `RowIndexOfReesMatrixSemigroupElement', 545
  `Row\-Index\-Of\-Rees\-Zero\-Matrix\-Semigroup\-Element', 545
  row spaces, 607
  Row Vectors over Finite Fields, \indexit{217}
  `Rules', 345
  Running GAP under MacOS, \indexit{31}
  `Runtime', 82
  `Runtimes', 81
\letter S
  $s_N$, 162
  `SameBlock', 743
  `SandwichMatrixOfReesMatrixSemigroup', 545
  `SandwichMatrixOfReesZeroMatrixSemigroup', 545
  save, 37
  `SaveOnExitFile', 73
  `SaveWorkspace', 37
  Saving and Loading a Workspace, \indexit{37}
  Saving a Pc Group, \indexit{458}
  saving on exit, 73
  `ScalarProduct', for characters, 778
  Schreier, 485
  Schreier-Sims, random, 420
  `SchurCover', 383
  Schur Covers and Multipliers, \indexit{383}
  Schur multiplier, 383
  scope, 43
  `ScriptFromString', 717
  Searching for Homomorphisms, \indexit{394}
  `SecHMSM', 260
  secondary subgroup generators, 500
  `SecondsDMYhms', 260
  `SeekPositionStream', 100
  Selecting a Different MeatAxe, \indexit{698}
  Selection Functions, \indexit{518}
  `SemidirectProduct', 506
  Semidirect Products, \indexit{506}
  `SemiEchelonBasis', 609
  `SemiEchelonBasisNC', 609
  `SemiEchelonMat', 232
  `SemiEchelonMatDestructive', 233
  `SemiEchelonMats', 233
  `SemiEchelonMatsDestructive', 233
  `SemiEchelonMatTransformation', 233
  `Semigroup', 539
  semigroup, 539
  `SemigroupByGenerators', 539
  `SemigroupByMultiplicationTable', 540
  `SemigroupIdealByGenerators', 541
  `SemigroupOfRewritingSystem', 554
  semiregular, 407
  Semisimple Lie Algebras and Root Systems, \indexit{646}
  `SemiSimpleType', 646
  sequence, Bernoulli, 148
    \sub Fibonacci, 155
    \sub Lucas, 156
  Series of Ideals, \indexit{644}
  `Set', 271
  `SetAssertionLevel', 81
  `SetCommutator', 456
  `SetConjugate', 456
  `SetCrystGroupDefaultAction', 435
  set difference, of collections, 276
  `SetEntrySCTable', 617
  `SetGasmanMessageStatus', 87
  `SetHelpViewer', 24
  `SetIndeterminateName', 670
  `SetInfoLevel', 80
  `SetName', 114
  Set Operations via Boolean Lists, \indexit{212}
  `SetParent', 291
  `SetPower', 456
  `SetPrintFormattingStatus', 102
  `SetRecursionTrapInterval', 86
  `SetReducedMultiplication', 465
  Sets, \indexit{110}
  sets, 173, 197
  Sets of Subgroups, \indexit{374}
  set stabilizer, 402
  `Setter', 122
  setter, 122
  Setter and Tester for Attributes, \indexit{122}
  `SetX', 207
  `ShallowCopy', 113
    \sub for lists, 181
  `ShiftedCoeffs', 221
  `ShiftedPadicNumber', 694
  Shifting and Trimming Coefficient Lists, \indexit{219}
  `ShortestVectors', 248
  `ShortLexOrdering', 284
  short vectors spanning a lattice, 246, 785
  `ShowArgument', 77
  `ShowArguments', 77
  `ShowDetails', 77
  `ShowImpliedFilters', 118
  `ShowMethods', 78
  `ShowOtherMethods', 78
  `ShrinkAllocationPlist', 183
  `ShrinkAllocationString', 253
  `ShrinkCoeffs', 222
  `ShrinkRowVector', 219
  `SiftedPcElement', 439
  `SiftedPermutation', 425
  `SiftedVector', 610
  `Sigma', 142
  sign, of an integer, 127
  Sign and Cycle Structure, \indexit{414}
  `SignInt', 127
  `SignPartition', 154
  `SignPerm', 414
  `SimpleLieAlgebra', 642
  `SimpleSystem', 647
  `SimplifiedFpGroup', 484
  SimplifiedFpGroup, \indexit{484}
  `SimplifyPresentation', 491
  `SimsNo', 529
  `SimultaneousEigenvalues', 239
  `SingleCollector', 456
  singlequote character, 252
  singlequotes, 250
  `SINT_CHAR', 258
  `Size', 274
    \sub for character tables, 736
    \sub for groups with pcgs, 451
  size, of a list or collection, 274
  `SizeBlist', 212
  `SizeConsiderFunction', 379
  `SizeNumbersPerfectGroups', 524
  `SizeOfFieldOfDefinition', 800
  `SizesCentralizers', 737
  `SizesConjugacyClasses', 737
  `SizeScreen', 76
  SizeScreen, \indexit{76}
  `SizesPerfectGroups', 523
  `SizeStabChain', 424
  `SL', 514
  smaller, associative words, 334
    \sub elements of finitely presented groups, 465
    \sub nonassociative words, 328
    \sub pcwords, 454
    \sub rational functions, 672
  `SmallerDegreePermutationRepresentation', 417
  smaller or equal, 47
  smaller test, 47
  `SmallestGeneratorPerm', 413
  `SmallestMovedPoint', 413
  `SmallestRootInt', 128
  `SmallGeneratingSet', 380
  `SmallGroup', 521
  Small Groups, \indexit{520}
  `SmallGroupsInformation', 522
  Smash MeatAxe Flags, \indexit{702}
  smith normal form, 851
  `SmithNormalFormIntegerMat', 243
  `SmithNormalFormIntegerMatTransforms', 243
  `SMTX.AbsoluteIrreducibilityTest', 701
  `SMTX.AlgEl', 702
  `SMTX.AlgElCharPol', 702
  `SMTX.AlgElCharPolFac', 702
  `SMTX.AlgElMat', 702
  `SMTX.AlgElNullspaceDimension', 702
  `SMTX.AlgElNullspaceVec', 702
  `SMTX.CentMat', 702
  `SMTX.CentMatMinPoly', 702
  `SMTX.CompleteBasis', 701
  `SMTX.Getter', 701
  `SMTX.GoodElementGModule', 701
  `SMTX.IrreducibilityTest', 701
  `SMTX.MatrixSum', 701
  `SMTX.MinimalSubGModule', 701
  `SMTX.MinimalSubGModules', 701
  `SMTX.RandomIrreducibleSubGModule', 701
  `SMTX.Setter', 701
  `SMTX.SortHomGModule', 701
  `SMTX.Subbasis', 702
  `SO', 515
  `Socle', 365
  `SocleTypePrimitiveGroup', 418
  `SolutionIntMat', 241
  `SolutionMat', 231
  `SolutionMatDestructive', 231
  `SolutionNullspaceIntMat', 241
  Some Remarks about Character Theory in GAP, \indexit{725}
  Some Special Algebras, \indexit{619}
  `Sort', 196
  `SortedCharacters', 761
  `SortedCharacterTable', 762
  Sorted Character Tables, \indexit{761}
  `SortedList', 271
  sorted list, 195
  Sorted Lists and Sets, \indexit{197}
  sorted lists as collections, 269
  `SortedSparseActionHomomorphism', 404
  `SortedTom', 707
  `Sortex', 196
  Sorting Lists, \indexit{196}
  `SortingPerm', 197
  Sorting Tables of Marks, \indexit{707}
  `SortParallel', 196
  `Source', 307
  `SourceOfIsoclinicTable', 760
  `SP', 515
  `Sp', 515
  space, 41
  `SparseActionHomomorphism', 404
  `SparseCartanMatrix', 648
  Special Characters, \indexit{252}
  special character sequences, 252
  Special Filenames, \indexit{93}
  Special Generating Sets, \indexit{380}
  `SpecialLinearGroup', 514
  Special Multiplication Algorithms for Matrices over GF(2), \indexit{239}
  `SpecialOrthogonalGroup', 515
  Special Pcgs, \indexit{448}
  `SpecialPcgs', attribute, 448
  Special Rules for Input Lines, \indexit{65}
  `SpecialUnitaryGroup', 515
  Specific and Parametrized Subgroups, \indexit{363}
  Specific Methods for Subgroup Lattice Computations, \indexit{377}
  `SplitCharacters', 756
  `SplitExtension', 460
  `SplitExtensions', 461
  `SplitString', 255
  `SplittingField', 674
  `Sqrt', 297
  square root, of an integer, 128
  `SquareRoots', 325
  `SSortedList', 271
  `StabChain', 422
  `StabChainBaseStrongGenerators', 423
  `StabChainImmutable', 422
  `StabChainMutable', 422
  `StabChainOp', 422
  `StabChainOptions', 423
  `Stabilizer', 402
  Stabilizer Chain Records, \indexit{423}
  Stabilizer Chains, \indexit{419}
  `StabilizerOfExternalSet', 410
  `StabilizerPcgs', 451
  Stabilizers, \indexit{402}
  `StandardAssociate', 569
  `StandardGeneratorsFunctions', 717
  `StandardGeneratorsInfo', for groups, 716
    \sub for tables of marks, 721
  `StandardGeneratorsOfGroup', 718
  Standard Generators of Groups, \indexit{716}
  Standardization of coset tables, \indexit{470}
  `StandardizeTable', 470
  `StarCyc', 164
  `State', 136
  Statements, \indexit{49}
  `StateRandom', 277
  `Stirling1', 148
  `Stirling2', 149
  Stirling number of the first kind, 148
  Stirling number of the second kind, 149
  `StoredGroebnerBasis', 687
  `StoreFusion', 808
  Storing Normal Subgroup Information, \indexit{765}
  `StraightLineProgElm', 343
  `StraightLineProgGens', 344
  `StraightLineProgram', 339
  Straight Line Program Elements, \indexit{343}
  `StraightLineProgramNC', 339
  Straight Line Programs, \indexit{339}
  `StraightLineProgramsTom', 719
  `StreamsFamily', 98
  `StretchImportantSLPElement', 344
  strictly sorted list, 195
  `String', 255
    \sub for cyclotomics, 159
  `StringDate', 260
  `StringOfResultOfStraightLineProgram', 341
  `StringPP', 255
  strings, equality of, 254
    \sub inequality of, 254
    \sub lexicographic ordering of, 254
  String Streams, \indexit{104}
  `StringTime', 260
  `StrongGeneratorsStabChain', 425
  `StronglyConnectedComponents', 317
  <Struct>, 288
  `<Struct>ByGenerators', 289
  `StructuralCopy', 113
    \sub for lists, 181
  structure constant, 747, 748
  `StructureConstantsTable', 605
  `StructureDescription', 355
  Structure Descriptions, \indexit{355}
  `<Struct>WithGenerators', 289
  `SU', 515
  `Subalgebra', 620
  `SubAlgebraModule', 636
  `SubalgebraNC', 620
  Subalgebras, \indexit{620}
  `SubalgebraWithOne', 620
  `SubalgebraWithOneNC', 621
  `SubdirectProduct', 508
  Subdirect Products, \indexit{508}
  `SubdirectProducts', 508
  subdomains, 292
  `Subfield', 580
  `SubfieldNC', 580
  `Subfields', 580
  Subfields of Fields, \indexit{580}
  `Subgroup', 352
  `SubgroupByPcgs', 442
  `SubgroupByProperty', 353
  subgroup fusions, 806
  subgroup generators tree, 500
  Subgroup Lattice, \indexit{375}
  `SubgroupNC', 352
  `SubgroupOfWholeGroupByCosetTable', 471
  `SubgroupOfWholeGroupByQuotientSubgroup', 476
  Subgroup Presentations, \indexit{485}
  `SubgroupProperty', 427
  Subgroups, \indexit{352}
  subgroups, polyhedral, 747
  Subgroups characterized by prime powers, \indexit{366}
  Subgroup Series, \indexit{370}
  `SubgroupShell', 353
  Subgroups of Polycyclic Groups - Canonical Pcgs, \indexit{442}
  Subgroups of Polycyclic Groups - Induced Pcgs, \indexit{441}
  `SubgroupsSolvableGroup', 378
  sublist, 175
    \sub access, 175
    \sub assignment, 177
    \sub operation, 176
  sublist assignment, operation, 178
  `Submagma', 321
  `SubmagmaNC', 321
  `SubmagmaWithInverses', 321
  `SubmagmaWithInversesNC', 321
  `SubmagmaWithOne', 321
  `SubmagmaWithOneNC', 321
  `Submodule', 575
  `SubmoduleNC', 575
  Submodules, \indexit{575}
  `Submonoid', 546
  `SubmonoidNC', 546
  `SubnearAdditiveGroup', 560
  `SubnearAdditiveGroupNC', 560
  `SubnearAdditiveMagma', 560
  `SubnearAdditiveMagmaNC', 560
  `SubnearAdditiveMagmaWithZero', 560
  `SubnearAdditiveMagmaWithZeroNC', 560
  `SubnormalSeries', 370
  `Subring', 563
  `SubringNC', 563
  `SubringWithOne', 567
  `SubringWithOneNC', 567
  Subroutines for the Construction of Class Fusions, \indexit{821}
  Subroutines for the Construction of Power Maps, \indexit{819}
  `Subsemigroup', 539
  `SubsemigroupNC', 539
  subsets, 149
  subset test, for collections, 275
  `Subspace', 599
  `SubspaceNC', 599
  `Subspaces', 601
  `SubstitutedWord', 336
  `SubsTom', 709
  `Sub<struct>', 292
  `Sub<struct>NC', 292
  `SubSyllables', 337
  subtract, a set from another, 199
  `SubtractBlist', 213
  subtraction, 48
    \sub matrices, 224
    \sub matrix and scalar, 224
    \sub rational functions, 671
    \sub scalar and matrix, 224
    \sub scalar and matrix list, 226
    \sub scalar and vector, 216
    \sub vector and scalar, 216
    \sub vectors, 216
  `SubtractSet', 199
  `Subword', 335
  `Successors', 316
  Suitability for Compilation, \indexit{36}
  `Sum', 205
  Sum and Intersection of Pcgs, \indexit{447}
  `SumFactorizationFunctionPcgs', 447
  `SumIntersectionMat', 234
  `SumX', 207
  `SupersolvableResiduum', 365
  `support', email address, 838
  `SupportedCharacterTableInfo', 729
  `SurjectiveActionHomomorphismAttr', 411
  `SuzukiGroup', 513
  `SylowComplement', 365
  `SylowSubgroup', 365
  Sylow Subgroups and Hall Subgroups, \indexit{365}
  `SylowSystem', 366
  Symbols, \indexit{40}
  Symmetric and Alternating Groups, \indexit{417}
  `SymmetricClosureBinaryRelation', 317
  `SymmetricGroup', 513
  symmetric group, powermap, 155
  `SymmetricParentGroup', 418
  `SymmetricParts', 790
  `SymmetricPowerOfAlgebraModule', 661
  symmetric relation, 316
  `Symmetrizations', 790
  symmetrizations, orthogonal, 790, 791
    \sub symplectic, 791
  Symmetrizations of Class Functions, \indexit{790}
  `SymplecticComponents', 791
  `SymplecticGroup', 515
  syntax errors, 64
  system getter, 121
  system setter, 121
  `Sz', 513
\letter T
  $t_N$, 162
  `TableAutomorphisms', 764
  table automorphisms, 810, 822
  table of chapters for help books, 23
  `TableOfMarks', 704
  `TableOfMarksByLattice', 705
  `TableOfMarksComponents', 708
  `TableOfMarksCyclic', 723
  `TableOfMarksDihedral', 723
  `TableOfMarksFamily', 708
  `TableOfMarksFrobenius', 723
  Table of Marks Objects in GAP, \indexit{704}
  table of sections for help books, 23
  tables, 725, 727
  tabulator, 41
  `Tau', 142
  Technical Details about Tables of Marks, \indexit{708}
  Technical Details about the Implementation of Magma Rings, \indexit{667}
  Technical Matters Concerning General Mappings, \indexit{313}
  `TemporaryGlobalVarName', 46
  `Tensored', 781
  `TensorProductGModule ', 697
  `TensorProductOfAlgebraModules', 660
  Tensor Products and Exterior and Symmetric Powers, \indexit{660}
  test, for a primitive root, 140
    \sub for a rational, 145
    \sub for records, 262
    \sub for set equality, 198
  `TestConsistencyMaps', 815
  `Tester', 122
  tester, 122
  Test Files, \indexit{84}
  `TestHomogeneous', 825
  `TestInducedFromNormalSubgroup', 827
  Testing Finiteness of Finitely Presented Groups, \indexit{480}
  Testing for the System Architecture, \indexit{35}
  Testing Monomiality, \indexit{827}
  `TestJacobi', 617
  `TestMonomial', 827
  `TestMonomialQuick', 828
  `TestMonomialUseLattice', 828
  Test of the installation, \indexit{834}
  `TestPackageAvailability', 848
  `TestPerm1', 797
  `TestPerm2', 797
  `TestPerm3', 797
  `TestPerm4', 797
  `TestPerm5', 797
  `TestQuasiPrimitive', 826
  `TestRelativelySM', 829
  Tests for Actions, \indexit{407}
  Tests for the Availability of Methods, \indexit{384}
  `TestSubnormallyMonomial', 829
  The .gaprc file, \indexit{33}
  The Adjoint Representation, \indexit{652}
  The Compiler, \indexit{35}
  The Defining Attributes of Rational Functions, \indexit{689}
  The Dixon-Schneider Algorithm, \indexit{754}
  The Documentation, \indexit{836}
  The External Representation for Associative Words, \indexit{339}
  The family pcgs, \indexit{454}
  The Interface between Character Tables and Groups, \indexit{731}
  The Interface between Tables of Marks and Character Tables, \indexit{721}
  The Library of Tables of Marks, \indexit{724}
  `then', 51
  The Natural Action, \indexit{416}
  The Pager Command, \indexit{25}
  The Permutation Image of an Action, \indexit{403}
  The Representations of Rational Functions, \indexit{688}
  The Smash MeatAxe, \indexit{701}
  The Syntax in BNF, \indexit{59}
  `ThreeGroup' library, 521
  Tietze Options, \indexit{503}
  Tietze Transformations, \indexit{490}
  Tietze Transformations that introduce new Generators, \indexit{495}
  `TietzeWordAbstractWord', 488
  `time', 82
  Timing, \indexit{81}
  Todd-Coxeter Procedure, \indexit{554}
  `Trace', 227
    \sub for field elements, 582
    \sub of a matrix, 227
  `TracedCosetFpGroup', 468
  `TraceImmediateMethods', 79
  `TraceMat', 227
  `TraceMethods', 79
  `TracePolynomial', 581
  Tracing generator images through Tietze transformations, \indexit{498}
  Tracing Methods, \indexit{79}
  `TransferDiagram', 815
  `Transformation', 555
  `TransformationData', 555
  `TransformationFamily', 555
  `TransformationNC', 555
  `TransformationRelation', 557
  `TransformationType', 555
  `TransformingPermutations', 764
  `TransformingPermutationsCharacterTables', 764
  transitive, 407
  `TransitiveClosureBinaryRelation', 317
  `TransitiveGroup', 519
  `TransitiveIdentification', 519
  Transitive Permutation Groups, \indexit{519}
  transitive relation, 316
  `Transitivity', for characters, 780
    \sub for class functions, 780
    \sub for group actions, 407
  `TranslatorSubalgebra', 639
  transporter, 403
  `TransposedMat', 228
  `TransposedMatAttr', 228
  `TransposedMatDestructive', 229
  `TransposedMatImmutable', 228
  `TransposedMatMutable', 228
  `TransposedMatOp', 228
  `TransposedMatrixGroup', 430
  Transversals, \indexit{358}
  Triangular Matrices, \indexit{235}
  `TriangulizedIntegerMat', 242
  `TriangulizedIntegerMatTransform', 242
  `TriangulizedNullspaceMat', 230
  `TriangulizedNullspaceMatDestructive', 230
  `TriangulizeIntegerMat', 242
  `TriangulizeMat', 230
  `TrivialCharacter', 776
  `TrivialGroup', 511
  `TrivialIterator', 280
  `TrivialSubalgebra', 621
  `TrivialSubgroup', 363
  `TrivialSubmagmaWithOne', 325
  `TrivialSubmodule', 575
  `TrivialSubmonoid', 546
  `TrivialSubnearAdditiveMagmaWithZero', 560
  `TrivialSubspace', 600
  `TryCosetTableInWholeGroup', 471
  `TryGcdCancelExtRepPolynomials', 691
  `Tuples', 151
  tuple stabilizer, 402
  `TwoClosure', 427
  `TwoCoboundaries', 459
  `TwoCocycles', 459
  `TwoCohomology', 459
  `TwoGroup' library, 521
  `TwoSidedIdeal', 564
  `TwoSidedIdealByGenerators', 565
  `TwoSidedIdealNC', 565
  `TwoSquares', 144
  type, boolean, 170
    \sub cyclotomic, 157
    \sub records, 262
    \sub strings, 250
  `TypeObj', 125
  `TypeOfDefaultGeneralMapping', 314
  Types, \indexit{125}
  `TzEliminate', 493
  `TzFindCyclicJoins', 494
  `TzGo', 491
  `TzGoGo', 492
  `TzImagesOldGens', 499
  `TzInitGeneratorImages', 498
  `TzNewGenerator', 490
  `TzOptions', 503
  `TzPreImagesNewGens', 499
  `TzPrint', 489
  `TzPrintGeneratorImages', 499
  `TzPrintGenerators', 488
  `TzPrintLengths', 489
  `TzPrintOptions', 504
  `TzPrintPairs', 489
  `TzPrintPresentation', 489
  `TzPrintRelators', 488
  `TzPrintStatus', 489
  `TzSearch', 493
  `TzSearchEqual', 494
  `TzSort', 482
  `TzSubstitute', 495
  `TzSubstituteCyclicJoins', 498
\letter U
  $u_N$, 162
  `UglyVector', 613
  `Unbind', 44
    \sub for lists, 179
  `UnbindGlobal', 45
  `UnderlyingCharacteristic', 738
  `UnderlyingCharacterTable', 770
  `UnderlyingElement', fp group elements, 466
    \sub fp semigroup elements, 552
  `Underlying\-Element\-Of\-Rees\-Matrix\-Semigroup\-Element', 545
  `Underlying\-Element\-Of\-Rees\-Zero\-Matrix\-Semigroup\-Element', 545
  `UnderlyingExternalSet', 411
  `UnderlyingFamily', 641
  `UnderlyingGeneralMapping', 307
  `UnderlyingGroup', for character tables, 732
    \sub for tables of marks, 710
  `UnderlyingLeftModule', 603
  `UnderlyingLieAlgebra', 647
  `UnderlyingMagma', 664
  `UnderlyingRelation', 307
  `UnInstallCharReadHookFunc', 106
  `Union', 276
  union, of collections, 276
    \sub of sets, 198
  `Union2', 276
  `UnionBlist', 212
  `Unique', 200
  `UniteBlist', 213
  `UniteBlistList', 213
  `UniteSet', 198
  `Units', 568
  Units and Factorizations, \indexit{568}
  `UnivariatenessTestRationalFunction', 675
  `UnivariatePolynomial', 674
  `UnivariatePolynomialByCoefficients', 674
  `UnivariatePolynomialRing', 683
  Univariate Polynomial Rings, \indexit{683}
  Univariate Polynomials, \indexit{674}
  `Univariate\-Rational\-Function\-By\-Coefficients', 680
  Univariate Rational Functions, \indexit{680}
  `UniversalEnvelopingAlgebra', 653
  Universal Enveloping Algebras, \indexit{653}
  UNIX, features, 27
    \sub options, 27
  `UNIXSelect', 98
  `Unknown', 168
  `UnloadSmallGroupsData', 522
  `UnorderedTuples', 150
  Unpacking, \indexit{832}
  `UnprofileFunctions', 83
  `UnprofileMethods', 83
  `until', 52
  `UntraceMethods', 79
  `UpdateMap', 813
  `UpEnv', 71
  `UpperCentralSeriesOfGroup', 372
  `UpperSubdiagonal', 235
  `UseBasis', 577
  `UseFactorRelation', 298
  Useful Categories for all Elements of a Family, \indexit{302}
  Useful Categories of Elements, \indexit{300}
  `UseIsomorphismRelation', 298
  User Streams, \indexit{103}
  `UseSubsetRelation', 298
  utilities for editing GAP files, 75
\letter V
  $v_N$, 162
  `Valuation', 694
  `Value', 677
  `ValueCochain', 656
  `ValueGlobal', 45
  `ValueMolienSeries', 793
  `ValueOption', 89
  `ValuePol', 221
  `ValuesOfClassFunction', 770
  Variable Access in a Break Loop, \indexit{71}
  Variables, \indexit{43}
  Vectors as coefficients of polynomials, \indexit{220}
  `VectorSpace', 599
  `Vector\-Space\-By\-Pcgs\-Of\-Elementary\-Abelian\-Group', 450
  Vector Space Homomorphisms, \indexit{610}
  Vector Spaces Handled By Nice Bases, \indexit{612}
  `vi', 75
  `View', 66
  View and Print, \indexit{66}
  `ViewObj', 67
    \sub for character tables, 748
    \sub for class functions, 774
    \sub for tables of marks, 706
  `vim', 75
  `VirtualCharacter', 775
  virtual character, 777
  virtual characters, 768
\letter W
  $w_N$, 162
  `WedgeGModule ', 697
  `WeekDay', 260
  `WeightLexOrdering', 284
  `WeightOfGenerators', 285
  `WeightsTom', 712
  `WeightVecFFE', 220
  `WeylGroup', 649
  `WeylOrbitIterator', 650
  `Where', 70
  While, \indexit{52}
  `while' loop, 52
  Whitespaces, \indexit{41}
  Why Class Functions?, \indexit{768}
  `WordAlp', 255
  words, in generators, 354
  Working with large degree permutation groups, \indexit{428}
  `WreathProduct', 508
  wreath product embedding, 509
  `WreathProductImprimitiveAction', 509
  `WreathProductOrdering', 286
  `WreathProductProductAction', 509
  Wreath Products, \indexit{508}
  `WriteAll', 101
  `WriteByte', 101
  `WriteLine', 101
\letter X
  $x_N$, 162
\letter Y
  $y_N$, 162
\letter Z
  `Z', 584
  `ZClassRepsQClass', 434
  `Zero', 294
  `ZeroAttr', 294
  `ZeroCoefficient', 665
  `ZeroCoefficientRatFun', 689
  `ZeroImmutable', 294
  `ZeroMapping', 306
  `ZeroMutable', 294
  `ZeroOp', 294
  `ZeroSameMutability', 294
  `ZeroSM', 294
  `ZippedProduct', 691
  `ZippedSum', 691
  `ZmodnZ', 135
  `ZmodnZObj', 135
  `ZmodpZ', 135
  `ZmodpZNC', 135
  `ZumbroichBase', 595
  `Zuppos', 377
