\letter {}
  (Near-)Additive Magma Categories, \indexit{550}
  (Near-)Additive Magma Generation, \indexit{551}
  `+', 48
  `-', 48
  `-A', 29
  `-B', 30
  `-C', 30
  `-D', 30
  `-K', 28
  `-L', 29
  `-M', 30
  `-N', 30
  `-O', 30
  `-P', 30
    \sub on Macintosh, 31
  `-R', 29
  `-T', 30
  `-U', 30
  `-W', 30
    \sub on Macintosh, 31
  `-X', 30
  `-Y', 30
  `-a', 29
    \sub on Macintosh, 31
  `-b', 27
  `-e', 27
    \sub on Macintosh, 31
  `-f', 27
    \sub on Macintosh, 31
  `-g', 28
  `-g -g', 28
  `-h', 27
  `-i', 30
  `-l', 28
  `-m', 28
  `-n', 27
    \sub on Macintosh, 31
  `-o', 28
    \sub on Macintosh, 31
  `-q', 27
  `-r', 29
  `-x', 27
  `-y', 28
  `-z', 30
    \sub on Macintosh, 31
  `.gaprc', 33
  `/', 48
    \sub for character tables, 723
  `\*', 48
    \sub for character tables, 723
  `\\\char 39', 247
  `\\XYZ', 247
  `\\\"', 247
  `\\\\', 247
  `\\b', 247
  `\\c', 247
  `\\in', operation for testing membership, 271
  `\\n', 247
  `\\r', 247
  `{\accent 94 }', 48
    \sub for class functions, 761
  1-Cohomology, \indexit{374}
  2-Cohomology and Extensions, \indexit{452}
\letter A
  `AbelianGroup', 504
  `AbelianInvariants', for character tables, 726
    \sub for groups, 363
  Abelian Invariants for Subgroups, \indexit{472}
  `AbelianInvariantsMultiplier', 377
  `AbelianInvariantsNormalClosureFpGroup', 473
  `Abelian\-Invariants\-Normal\-Closure\-Fp\-Group\-Rrs', 473
  `AbelianInvariantsOfList', 239
  `AbelianInvariantsSubgroupFpGroup', 472
  `AbelianInvariantsSubgroupFpGroupMtc', 472
  `AbelianInvariantsSubgroupFpGroupRrs', 472
  `AbelianNumberField', 582
  abelian number field, 583
  abelian number fields, canonicalbasis, 585
  abelian number fields, Galois group, 586
  `AbelianSubfactorAction', 399
  About Group Actions, \indexit{391}
  `AbsInt', 127
  `AbsoluteIrreducibleModules', 742
  `AbsoluteValue', 157
  absolute value of an integer, 127
  `AbsolutIrreducibleModules', 742
  abstract word, 321
  `AbstractWordTietzeWord', 481
  accessing, list elements, 172
    \sub record elements, 257
  Accessing a Module, \indexit{687}
  Accessing Record Elements, \indexit{257}
  Accessing Subgroups via Tables of Marks, \indexit{708}
  `AClosestVectorCombinationsMatFFEVecFFE', 215
  `AClosest\-Vector\-Combinations\-Mat\-FFEVec\-FFECoords', 215
  `ActingAlgebra', 625
  `ActingDomain', 403
  Acting OnRight and OnLeft, \indexit{428}
  `Action', 398
  action, by conjugation, 392
    \sub on blocks, 392
    \sub on sets, 392
  `ActionHomomorphism', 397
  Action of a group on itself, \indexit{399}
  Action on Subfactors Defined by a Pcgs, \indexit{443}
  actions, 392
  Actions of Matrix Groups, \indexit{425}
  `ActorOfExternalSet', 405
  `Add', 175
  add, an element to a set, 193
  `AddCoeffs', 213
  `AddGenerator', 483
  `AddGenerators', 340
  `AddGeneratorsExtendSchreierTree', 420
  addition, 48
    \sub list and non-list, 183
    \sub matrices, 219
    \sub matrix and scalar, 219
    \sub operation, 292
    \sub rational functions, 661
    \sub scalar and matrix, 219
    \sub scalar and matrix list, 220
    \sub scalar and vector, 211
    \sub vector and scalar, 211
    \sub vectors, 210
  Additive Arithmetic for Lists, \indexit{182}
  `AdditiveInverse', 290
  `AdditiveInverseAttr', 290
  `AdditiveInverseImmutable', 290
  `AdditiveInverseMutable', 290
  `AdditiveInverseOp', 290
  `AdditiveInverseSameMutability', 290
  `AdditiveInverseSM', 290
  `AdditiveNeutralElement', 552
  `AddRelator', 483
  `AddRowVector', 213
  `AddRule', 340
  `AddRuleReduced', 340
  `AddSet', 193
  `AdjointAssociativeAlgebra', 642
  `AdjointBasis', 614
  `AdjointMatrix', 642
  `AdjointModule', 626
  Advanced Features of GAP, \indexit{29}
  Advanced List Manipulations, \indexit{201}
  Advanced Methods for Dixon-Schneider Calculations, \indexit{743}
  `AffineAction', 444
  `AffineActionLayer', 444
  `AffineOperation', 444
  `AffineOperationLayer', 444
  `Agemo', 360
  `Algebra', 605
  `AlgebraByStructureConstants', 608
  `AlgebraGeneralMappingByImages', 619
  `AlgebraHomomorphismByImages', 619
  `AlgebraHomomorphismByImagesNC', 619
  `AlgebraicExtension', 682
  `AlgebraWithOne', 605
  `AlgebraWithOneGeneralMappingByImages', 619
  `AlgebraWithOneHomomorphismByImages', 620
  `AlgebraWithOneHomomorphismByImagesNC', 620
  `AllBlocks', 402
  `AllIrreducibleSolvableGroups', 522
  `All<Library>Groups', 510
  `AllPrimitiveGroups', 510
  `AllSmallGroups', 513
  `AllTransitiveGroups', 510
  `Alpha', 812
  `AlternatingGroup', 504
  `and', 168
    \sub for filters, 117, 169
  An Example of Advanced Dixon-Schneider Calculations, \indexit{744}
  `ANFAutomorphism', 587
  `AntiSymmetricParts', 778
  antisymmetric relation, 311
  `Append', 175
  `AppendTo', 95
    \sub for streams, 101
  Apple, 828, 829
  `ApplicableMethod', 77
  ApplicableMethod, \indexit{77}
  `ApplicableMethodTypes', 77
  `Apply', 196
  `ApplySimpleReflection', 639
  `ApproximateSuborbitsStabilizerPermGroup', 419
  `ARCH_IS_MAC', 34
  `ARCH_IS_UNIX', 34
  `ARCH_IS_WINDOWS', 34
  `arg', special function argument, 46, 56
  Arithmetic for External Representations of Polynomials, \indexit{680}
  Arithmetic for Lists, \indexit{180}
  Arithmetic Operations for Class Functions, \indexit{759}
  Arithmetic Operations for Elements, \indexit{292}
  Arithmetic Operations for General Mappings, \indexit{304}
  Arithmetic Operators, \indexit{48}
  `Arrangements', 147
  arrow notation for functions, 57
  `AsAlgebra', 614
  `AsAlgebraWithOne', 615
  `AsBinaryRelationOnPoints', 312
  `AsBlockMatrix', 234
  `AscendingChain', 366
  `AsDivisionRing', 571
  `AsDuplicateFreeList', 195
  `AsField', 571
  `AsFreeLeftModule', 568
  `AsGroup', 345
  `AsGroupGeneralMappingByImages', 380
  `AsLeftIdeal', 558
  `AsLeftModule', 566
  `AsList', 267
  `AsMagma', 316
  `AsMonoid', 538
  `AsPolynomial', 663
  `AsRightIdeal', 558
  `AsRing', 555
  `AsSemigroup', 531
  `Assert', 80
  `AssertionLevel', 80
  Assertions, \indexit{80}
  `AsSet', 267
  `AssignGeneratorVariables', 328
  assignment, to a list, 173
    \sub to a record, 258
    \sub variable, 49
  Assignments, \indexit{49}
  `AssignNiceMonomorphismAutomorphismGroup', 387
  `AssociatedPartition', 152
  `AssociatedReesMatrixSemigroupOfDClass', 537
  `Associates', 561
  associativity, 48
  `AssocWordByLetterRep', 333
  `AsSortedList', 267
  `AsSSortedList', 267
  `As<Struct>', 284
  `AsSubalgebra', 615
  `AsSubalgebraWithOne', 615
  `AsSubgroup', 346
  `AsSubgroupOfWholeGroupByQuotient', 470
  `AsSubmagma', 316
  `AsSubmonoid', 538
  `AsSubsemigroup', 531
  `AsSubspace', 590
  `AsSub<struct>', 287
  `AsTransformation', 548
  `AsTransformationNC', 548
  `AsTwoSidedIdeal', 558
  `AsVectorSpace', 589
  at exit functions, 72
  ATLAS Irrationalities, \indexit{159}
  `AtlasIrrationality', 161
  atomic irrationalities, 159
  Attributes, \indexit{121}
  Attributes and Operations for Algebras, \indexit{613}
  Attributes and Properties for (Near-)Additive Magmas, \indexit{552}
  Attributes and Properties for Collections, \indexit{268}
  Attributes and Properties for Magmas, \indexit{318}
  Attributes and Properties for Matrix Groups, \indexit{424}
  Attributes and Properties of Character Tables, \indexit{724}
  Attributes and Properties of Elements, \indexit{288}
  Attributes of and Operations on Equivalence Relations, \indexit{313}
  Attributes of Tables of Marks, \indexit{698}
  `AttributeValueNotSet', 122
  `AugmentationIdeal', 654
  `AugmentedCosetTableInWholeGroup', 465
  `AugmentedCosetTableMtc', 465
  `AugmentedCosetTableRrs', 465
  Augmented Coset Tables and Rewriting, \indexit{465}
  automatic loading of gap packages, 834
  `AutomorphismDomain', 386
  `AutomorphismGroup', 386
    \sub for groups with pcgs, 445
  automorphism group, of number fields, 586
  Automorphisms and Equivalence of Character Tables, \indexit{751}
  `AutomorphismsOfTable', 727
\letter B
  $b_N$, 159
  backslash character, 247
  backspace character, 247
  `Backtrace', GAP3 name for `Where', 70
  Backtrack, \indexit{421}
  `BANNER', 839
  `BaseFixedSpace', 226
  `BaseIntersectionIntMats', 236
  `BaseIntMat', 236
  `BaseMat', 228
  `BaseMatDestructive', 228
  `BaseOfGroup', 418
  `BaseOrthogonalSpaceMat', 229
  Bases of Vector Spaces, \indexit{591}
  `BaseStabChain', 418
  `BaseSteinitzVectors', 229
  Basic Actions, \indexit{392}
  Basic Groups, \indexit{503}
  Basic Operations for Class Functions, \indexit{758}
  Basic Operations for Lists, \indexit{171}
  `BasicWreathProductOrdering', 280
  `Basis', 592
  `BasisNC', 592
  `BasisVectors', 593
  `Bell', 145
  `Bernoulli', 146
  `BestQuoInt', 129
  `BestSplittingMatrix', 744
  `BiAlgebraModule', 623
  `BiAlgebraModuleByGenerators', 623
  `BilinearFormMat', 637
  binary relation, 310
  `BinaryRelationByElements', 310
  `BinaryRelationOnPoints', 311
  `BinaryRelationOnPointsNC', 311
  Binary Relations on Points, \indexit{311}
  `BinaryRelationTransformation', 549
  `BindGlobal', 45
  `Binomial', 145
  blank, 40
  `BlistList', 206
  Block Matrices, \indexit{234}
  `BlockMatrix', 234
  `Blocks', 402
  `BlocksInfo', 732
  Block Systems, \indexit{402}
  `BlownUpMat', 231
  `BlownUpVector', 231
  `BlowUpIsomorphism', 425
  BNF, 58
  body, 55
  `BombieriNorm', 669
  Boolean Lists Representing Subsets, \indexit{206}
  bound, 42
  Brauer character, 765
  `BrauerCharacterValue', 788
  `BrauerTable', 718
  `BrauerTableOp', 718
  `BravaisGroup', 428
  `BravaisSubgroups', 428
  `BravaisSupergroups', 428
  Break, \indexit{54}
  break loop message, 69
  Break Loops, \indexit{67}
  `break' statement, 54
  browsing backwards, 22
  browsing backwards one chapter, 22
  browsing forward, 22
  browsing forward one chapter, 22
  browsing the next section browsed, 22
  browsing the previous section browsed, 22
  Browsing through the Sections, \indexit{22}
  bug reports, see If Things Go Wrong, 826
  Building new orderings, \indexit{276}
\letter C
  $c_N$, 159
  Calculating with Group Automorphisms, \indexit{387}
  Calendar Arithmetic, \indexit{254}
  `CallFuncList', 62
  Calling a function with a list argument that is interpreted as several arguments, \indexit{62}
  Cancellation Tests for Rational Functions, \indexit{680}
  `CanComputeIndex', 378
  `CanComputeIsSubset', 378
  `CanComputeSize', 377
  `CanComputeSizeAnySubgroup', 378
  candidates, for permutation characters, 781, 783
  `CanEasilyCompareElements', 291
  `CanEasilyCompareElementsFamily', 291
  `CanEasilyComputePcgs', 431
  `CanEasilySortElements', 291
  `CanEasilySortElementsFamily', 291
  `CanEasilyTestMembership', 377
  `CanonicalBasis', 592
  canonical basis, for matrix spaces, 599
    \sub for row spaces, 599
  `CanonicalGenerators', 637
  `CanonicalPcElement', 433
  `CanonicalPcgs', 436
  `CanonicalPcgsByGeneratorsWithImages', 438
  `Canonical\-Representative\-Determinator\-Of\-External\-Set', 405
  `CanonicalRepresentativeOfExternalSet', 404
  `CanonicalRightCosetElement', 352
  Carmichael's lambda function, 136
  carriage return character, 247
  `CartanMatrix', 637
  `CartanSubalgebra', 634
  `Cartesian', 197
  Categories, \indexit{118}
  Categories and Properties of Algebras, \indexit{612}
  Categories for Streams and the StreamsFamily, \indexit{97}
  Categories of Associative Words, \indexit{326}
  Categories of Matrices, \indexit{218}
  `CategoriesOfObject', 120
  Categories of Words and Nonassociative Words, \indexit{321}
  `CategoryCollections', 263
  `Center', 319
  center, 318
  `CentralCharacter', 768
  central character, 768
  `CentralIdempotentsOfAlgebra', 617
  centraliser, 318
  `Centralizer', 318
    \sub for groups with pcgs, 445
  `CentralizerInGLnZ', 428
  `CentralizerModulo', 367
  `CentralizerSizeLimitConsiderFunction', 446
  `CentralNormalSeriesByPcgs', 439
  `Centre', 319
    \sub for groups with pcgs, 445
  centre, of a character, 767
  `CentreOfCharacter', 767
  `CF', 582
  `ChangeStabChain', 420
  Changing Presentations, \indexit{482}
  Changing the Help Viewer, \indexit{23}
  Changing the Representation, \indexit{285}
  Changing the Structure, \indexit{284}
  `CHAR_INT', 252
  `CHAR_SINT', 253
  `Character', 763
  Character Conversion, \indexit{252}
  `CharacterDegrees', 724
  Character Degrees and Derived Length, \indexit{812}
  `Characteristic', 288
  characteristic, for class functions, 762
  `CharacteristicPolynomial', 230
  characteristic polynomial, for field elements, 573
  `CharacterNames', 728
  characters, 756
    \sub permutation, 781, 783
    \sub symmetrizations of, 777
  `CharacterTable', 718
  Character Table Categories, \indexit{719}
  `CharacterTableDirectProduct', 746
  `CharacterTableFactorGroup', 747
  `CharacterTableIsoclinic', 748
  character tables, 717
    \sub access to, 717
    \sub calculate, 717
    \sub infix operators, 723
    \sub of groups, 717
  `CharacterTableWithSortedCharacters', 749
  `CharacterTableWithSortedClasses', 749
  `CharacterTableWreathSymmetric', 748
  character value, of group element using powering operator, 761
  `CharsFamily', 248
  `CheckFixedPoints', 802
  `CheckForHandlingByNiceBasis', 604
  `CheckPermChar', 809
  `ChevalleyBasis', 636
  `ChiefNormalSeriesByPcgs', 440
  `ChiefSeries', 364
  `ChiefSeriesThrough', 364
  `ChiefSeriesUnderAction', 364
  `ChineseRem', 130
  Chinese remainder, 130
  `Chomp', 252
  `CIUnivPols', 661
  `ClassElementLattice', 369
  classes, real, 729
  `ClassesSolvableGroup', 445
  `ClassFunction', 763
  class function, 756
  class function objects, 756
  class functions, 799
    \sub as ring elements, 760
  `ClassFunctionSameType', 764
  Class Fusions between Character Tables, \indexit{794}
  Classical Groups, \indexit{505}
  `ClassMultiplicationCoefficient', for character tables, 736
  class multiplication coefficient, 736, 737
  `ClassNames', 728
  `ClassNamesTom', 700
  `ClassOrbit', 729
  `ClassPermutation', 750
  `ClassPositionsOfAgemo', 730
  `ClassPositionsOfCentre', for characters, 767
    \sub for character tables, 730
  `ClassPositionsOfDerivedSubgroup', 730
  `Class\-Positions\-Of\-Direct\-Product\-Decompositions', 730
  `ClassPositionsOfElementaryAbelianSeries', 730
  `ClassPositionsOfFittingSubgroup', 730
  `ClassPositionsOfKernel', 767
  `ClassPositionsOfLowerCentralSeries', 730
  `ClassPositionsOfMaximalNormalSubgroups', 730
  `ClassPositionsOfNormalClosure', 730
  `ClassPositionsOfNormalSubgroup', 754
  `ClassPositionsOfNormalSubgroups', 730
  `ClassPositionsOfSupersolvableResiduum', 730
  `ClassPositionsOfUpperCentralSeries', 730
  `ClassRoots', 729
  `ClassStructureCharTable', 736
  `ClassTypesTom', 699
  `CleanedTailPcElement', 433
  `ClearCacheStats', 83
  `ClearProfile', 82
  clone, an object, 114
  `CloseMutableBasis', 597
  `CloseStream', 98
  `ClosureGroup', 347
  `ClosureGroupAddElm', 348
  `ClosureGroupCompare', 348
  `ClosureGroupDefault', 348
  `ClosureGroupIntest', 348
  `ClosureLeftModule', 567
  `ClosureNearAdditiveGroup', 552
  Closure Operations and Other Constructors, \indexit{312}
  `ClosureRing', 555
  Closures of (Sub)groups, \indexit{347}
  `Closure<Struct>', 284
  `ClosureSubgroup', 348
  `ClosureSubgroupNC', 348
  `Coboundaries', 647
  `Cochain', 646
  `CochainSpace', 646
  `Cocycles', 647
  cocycles, 374
  `CodePcGroup', 456
  `CodePcgs', 455
  Coding a Pc Presentation, \indexit{455}
  coefficient, binomial, 145
  Coefficient List Arithmetic, \indexit{213}
  `Coefficients', 593
  coefficients, for cyclotomics, 157
  `CoefficientsAndMagmaElements', 655
  `CoefficientsFamily', 677
  `CoefficientsMultiadic', 130
  `CoefficientsOfLaurentPolynomial', 669
  `CoefficientsOfUnivariatePolynomial', 663
  `Coefficients\-Of\-Univariate\-Rational\-Function', 663
  `CoefficientsQadic', 130
  `CoefficientsRing', 670
  `CoeffsCyc', 157
  `CoeffsMod', 214
  cohomology, 374
  `COHORTS_PRIMITIVE_GROUPS', 520
  `CoKernelOfAdditiveGeneralMapping', 307
  `CoKernelOfMultiplicativeGeneralMapping', 306
  `CollapsedMat', 805
  `Collected', 195
  Collection Families, \indexit{263}
  `CollectionsFamily', 263
  Coloring the Prompt and Input, \indexit{37}
  `ColorPrompt', 38
  `ColumnIndexOfReesMatrixSemigroupElement', 537
  `Column\-Index\-Of\-Rees\-Zero\-Matrix\-Semigroup\-Element', 537
  `Combinations', 147
  Combinations, Arrangements and Tuples, \indexit{147}
  `CombinatorialCollector', 450
  Combinatorial Numbers, \indexit{145}
  `Comm', 292
    \sub for words, 329
  Command Line Options, \indexit{27}
  comments, 40
  `CommutativeDiagram', 802
  `CommutatorFactorGroup', 367
  `CommutatorLength', 357
    \sub for character tables, 726
  `CommutatorSubgroup', 357
  `Compacted', 195
  `CompanionMat', 231
  `CompareVersionNumbers', 837
  comparison, fp semigroup elements, 543
    \sub operation, 291
    \sub rational functions, 661
  Comparison of Associative Words, \indexit{329}
  Comparison of Class Functions, \indexit{759}
  Comparison of Elements of Finitely Presented Groups, \indexit{458}
  Comparison of Elements of Finitely Presented Semigroups, \indexit{543}
  Comparison of Permutations, \indexit{407}
  Comparison of Rational Functions, \indexit{661}
  Comparison of Words, \indexit{322}
  Comparison Operations for Elements, \indexit{291}
  Comparisons, \indexit{47}
  comparisons, of booleans, 167
    \sub of lists, 179
  Comparisons of Booleans, \indexit{167}
  Comparisons of Cyclotomics, \indexit{159}
  Comparisons of Lists, \indexit{179}
  Comparisons of Records, \indexit{260}
  Comparisons of Strings, \indexit{249}
  `CompatibleConjugacyClasses', 722
  `CompatiblePairs', 454
  Compilation, \indexit{821}
  Compiling Library Code, \indexit{35}
  `Complementclasses', 357
  `ComplementclassesEA', 376
  `ComplementIntMat', 237
  `ComplementSystem', 360
  Completion Files, \indexit{33}
  `ComplexConjugate', 162
    \sub for class functions, 762
  `ComplexificationQuat', 609
  Components of a Dixon Record, \indexit{744}
  `CompositionMapping', 300
    \sub for Frobenius automorphisms, 580
  `CompositionMapping2', 300
  `CompositionMaps', 799
  `CompositionOfStraightLinePrograms', 337
  `CompositionSeries', 364
    \sub for groups with pcgs, 445
  `ComputedBrauerTables', 718
  `ComputedClassFusions', 795
  `ComputedIndicators', 735
  `ComputedIsPSolvableCharacterTables', 735
  `ComputedPowerMaps', 791
  `ComputedPrimeBlockss', 731
  Computing a Pcgs, \indexit{430}
  Computing a Permutation Representation, \indexit{410}
  Computing Pc Groups, \indexit{451}
  Computing Possible Permutation Characters, \indexit{783}
  Computing the Irreducible Characters of a Group, \indexit{740}
  `Concatenation', 195
  concatenation, of lists, 195
  `Conductor', 157
  `ConfluentRws', 340
  `Congruences', for character tables, 807
  Congruences for semigroups, \indexit{533}
  `ConjugacyClass', 354
  Conjugacy Classes, \indexit{354}
  `ConjugacyClasses', attribute, 354
    \sub for character tables, 721
    \sub for groups with pcgs, 445
    \sub for linear groups, 508
  `ConjugacyClassesByOrbits', 355
  `ConjugacyClassesByRandomSearch', 355
  Conjugacy Classes in Classical Groups, \indexit{508}
  Conjugacy Classes in Solvable Groups, \indexit{445}
  `ConjugacyClassesMaximalSubgroups', 368
  `ConjugacyClassesPerfectSubgroups', 371
  `ConjugacyClassesSubgroups', 368
  `ConjugacyClassSubgroups', 367
  conjugate, matrix, 220
    \sub of a word, 329
  `ConjugateDominantWeight', 639
  `ConjugateDominantWeightWithWord', 639
  `ConjugateGroup', 345
  `Conjugates', 574
  `ConjugateSubgroup', 347
  `ConjugateSubgroups', 347
  conjugation, 392
  `ConjugatorAutomorphism', 384
  `ConjugatorAutomorphismNC', 384
  `ConjugatorIsomorphism', 384
  `ConjugatorOfConjugatorIsomorphism', 385
  `ConnectGroupAndCharacterTable', 722
  `ConsiderKernels', 807
  `ConsiderSmallerPowerMaps', 808
  `ConsiderStructureConstants', 799
  `ConsiderTableAutomorphisms', 810
  `ConstantTimeAccessList', 191
  constituent, of a group character, 766
  `ConstituentsCompositionMapping', 300
  `ConstituentsOfCharacter', 767
  Constructing Algebras as Free Algebras, \indexit{606}
  Constructing Algebras by Generators, \indexit{605}
  Constructing Algebras by Structure Constants, \indexit{607}
  Constructing Character Tables from Others, \indexit{746}
  Constructing Domains, \indexit{283}
  Constructing Lie algebras, \indexit{631}
  Constructing Pc Groups, \indexit{449}
  Constructing Subdomains, \indexit{287}
  Constructing Tables of Marks, \indexit{694}
  Constructing Vector Spaces, \indexit{589}
  Construction of Abelian Number Fields, \indexit{582}
  Construction of Stabilizer Chains, \indexit{415}
  Constructors for Basic Groups, \indexit{509}
  `ContainedCharacters', 806
  `ContainedDecomposables', 806
  `ContainedMaps', 801
  `ContainedPossibleCharacters', 804, 805
  `ContainedPossibleVirtualCharacters', 804, 805
  `ContainedSpecialVectors', 804, 805
  `ContainedTom', 704
  `ContainingTom', 704
  `ContinuedFractionApproximationOfRoot', 141
  `ContinuedFractionExpansionOfRoot', 141
  Continued Fractions, \indexit{141}
  `continue' statement, 55
  Conventions for Character Tables, \indexit{721}
  convert, to a string, 248
  Converting Groups to Finitely Presented Groups, \indexit{466}
  `ConvertToCharacterTable', 719
  `ConvertToCharacterTableNC', 719
  `ConvertToMatrixRep', 232
  `ConvertToMatrixRepNC', 232
  `ConvertToRangeRep', 204
  `ConvertToStringRep', 248
  `ConvertToTableOfMarks', 698
  `ConvertToVectorRep', 212
  `ConvertToVectorRepNC', 212
  `ConwayPolynomial', 580
  Conway Polynomials, \indexit{580}
  coprime, 48
  copy, 114
    \sub an object, 114
  `CopyOptionsDefaults', 420
  Copyrights, \indexit{833}
  `CopyStabChain', 419
  `Core', 356
  `CorrespondingGeneratorsByModuloPcgs', 438
  coset, 351
  `CosetLeadersMatFFE', 215
  Cosets, \indexit{351}
  `CosetTable', 461
  `CosetTableBySubgroup', 462
  `CosetTableDefaultLimit', 463
  `CosetTableDefaultMaxLimit', 462
  `CosetTableFromGensAndRels', 462
  `CosetTableInWholeGroup', 465
  `CosetTableOfFpSemigroup', 546
  Coset Tables and Coset Enumeration, \indexit{461}
  Coset tables for subgroups in the whole group, \indexit{465}
  `CosetTableStandard', 464
  CRC, 36
  `CrcFile', 95
    \sub example, 36
  CRC Numbers, \indexit{36}
  `CreateCompletionFiles', 34
  `CreateCompletionFilesPkg', 838
  Creating Character Tables, \indexit{717}
  Creating Class Functions from Values Lists, \indexit{763}
  Creating Class Functions using Groups, \indexit{764}
  Creating Finite Fields, \indexit{578}
  Creating Finitely Presented Groups, \indexit{458}
  Creating Finitely Presented Semigroups, \indexit{542}
  Creating Group Homomorphisms, \indexit{379}
  Creating Groups, \indexit{344}
  Creating Mappings, \indexit{299}
  Creating Permutations, \indexit{408}
  Creating Presentations, \indexit{475}
  Creation of Algebraic Extensions, \indexit{682}
  Creation of Rational Functions, \indexit{679}
  Credit, \indexit{21}
  `CrystGroupDefaultAction', 429
  `Cycle', 400
  `CycleLength', 400
  `CycleLengths', 400
  `Cycles', 400
  `CycleStructureClass', 768
  `CycleStructurePerm', 408
  `CyclicExtensionsTom', 704
  `CyclicGroup', 503
  `CyclotomicField', 582
  cyclotomic field elements, 155
  cyclotomic fields, canonicalbasis, 584
  `CyclotomicPolynomial', 667
  Cyclotomic Polynomials, \indexit{667}
  `Cyclotomics', 155
  cyclotomics, defaultfield, 583
\letter D
  $d_N$, 159
  Darstellungsgruppe, see `EpimorphismSchurCover', 376
  `DataType', 125
  data type, unknown, 165
  `DayDMY', 254
  `DaysInMonth', 254
  `DaysInYear', 254
  Debugging Recursion, \indexit{84}
  DEC, 240
  `DeclareAutoPackage', 838
  `DeclareHandlingByNiceBasis', 603
  `DeclareInfoClass', 79
  `DeclarePackage', 838
  `DeclarePackageAutoDocumentation', 838
  `DeclarePackageDocumentation', 838
  `DecodeTree', 492
  DecodeTree, \indexit{492}
  decompose, a group character, 766
  `DecomposedFixedPointVector', 704
  `DecomposeTensorProduct', 647
  `Decomposition', 240
  `DecompositionInt', 241
  `DecompositionMatrix', 733
  decomposition matrix, 240
  Decompositions, \indexit{240}
  `Decreased', 775
  `DefaultField', 570
    \sub for cyclotomics, 158
    \sub for finite field elements, 578
  `DefaultFieldByGenerators', 571
  `DefaultFieldOfMatrix', 221
  `DefaultFieldOfMatrixGroup', 424
  `DefaultRing', 554
    \sub for finite field elements, 578
  `DefaultRingByGenerators', 555
  `DefaultStabChainOptions', 417
  Defining a Pcgs Yourself, \indexit{431}
  `DefiningPolynomial', 572
  `DefiningQuotientHomomorphism', 470
  `DegreeFFE', 577
  `DegreeIndeterminate', 665
  `DegreeOfBinaryRelation', 311
  `DegreeOfCharacter', 766
  `DegreeOfLaurentPolynomial', 664
  `DegreeOfTransformation', 547
  `DegreeOfTransformationSemigroup', 533
  `DegreeOverPrimeField', 572
  `Delta', 813
  denominator, of a rational, 144
  `DenominatorCyc', 157
  `DenominatorOfModuloPcgs', 437
  `DenominatorOfRationalFunction', 662
  `DenominatorRat', 144
  deprecated, 838
  `DepthOfPcElement', 433
  `DepthOfUpperTriangularMatrix', 230
  `Derangements', 149
  `Derivations', 632
  `Derivative', 666
  `DerivedLength', 365
  `DerivedSeriesOfGroup', 365
  `DerivedSubgroup', 357
  `DerivedSubgroupsTom', 703
  `DerivedSubgroupsTomPossible', 703
  `DerivedSubgroupsTomUnique', 703
  `DerivedSubgroupTom', 703
  `DescriptionOfRootOfUnity', 158
  `Determinant', 221
  determinant character, 768
  `DeterminantIntMat', 240
  `DeterminantMat', 221
  `DeterminantMatDestructive', 222
  `DeterminantMatDivFree', 222
  Determinant of an integer matrix, \indexit{240}
  `DeterminantOfCharacter', 768
  Developing rewriting systems, \indexit{342}
  `DiagonalizeIntMat', 238
  `DiagonalizeMat', 227
  `DiagonalMat', 223
  `DiagonalOfMat', 229
  `Difference', 271
  `DifferenceBlist', 207
  `DihedralGroup', 504
  `Dimension', 568
  `DimensionOfHighestWeightModule', 648
  `DimensionOfMatrixGroup', 424
  `DimensionOfVectors', 598
  `DimensionsLoewyFactors', 366
  `DimensionsMat', 221
  Directories, \indexit{91}
  `DirectoriesLibrary', 91
  `DirectoriesPackageLibrary', 836
  `DirectoriesPackagePrograms', 836
  `DirectoriesSystemPrograms', 92
  `Directory', 91
  `DirectoryContents', 92
  `DirectoryCurrent', 91
  `DirectoryTemporary', 91
  `DirectProduct', 498
  `DirectProductOp', 498
  Direct Products, \indexit{498}
  `DirectSumDecomposition', 617
    \sub for Lie algebras, 636
  Direct Sum Decompositions, \indexit{635}
  `DirectSumOfAlgebraModules', 628
    \sub for Lie algebras, 651
  `DirectSumOfAlgebras', 616
  `DisableAttributeValueStoring', 123
  disable automatic loading, 834
  `Discriminant', 666
  `Display', 66
    \sub for character tables, 737, 762
    \sub for tables of marks, 696
  `DisplayCacheStats', 83
  `DisplayCompositionSeries', 364
  `DisplayEggBoxOfDClass', 535
  `DisplayImfInvariants', 524
  `DisplayInformationPerfectGroups', 517
  `DisplayOptions', 738
  `DisplayOptionsStack', 89
  `DisplayProfile', 82
  `DisplayRevision', 83
  `DistancesDistributionMatFFEVecFFE', 214
  `DistancesDistributionVecFFEsVecFFE', 214
  `DistanceVecFFE', 214
  Distinguished Subalgebras, \indexit{633}
  division, 48
    \sub operation, 292
  `DivisionRingByGenerators', 571
  division rings, 570
  divisors, of an integer, 133
  `DivisorsInt', 133
  Dixon-Schneider algorithm, 742
  `DixonInit', 743
  `DixonRecord', 743
  `DixonSplit', 743
  `DixontinI', 743
  `DMYDay', 254
  `DMYhmsSeconds', 255
  `DnLattice', 776
  `DnLatticeIterative', 777
  `do', 52
  document formats (text, dvi, ps, pdf, html), 23
  `Domain', 288
  `DomainByGenerators', 288
  Domain Categories, \indexit{285}
  Domains, \indexit{111}
  Domains Generated by Class Functions, \indexit{789}
  Domains of Subspaces of Vector Spaces, \indexit{590}
  `DominantCharacter', 647
  `DominantWeights', 647
  `DoubleCoset', 353
  `DoubleCosetRepsAndSizes', 354
  Double Cosets, \indexit{353}
  `DoubleCosets', operation, 353
  `DoubleCosetsNC', operation, 353
  doublequote character, 247
  doublequotes, 245
  `DownEnv', 70
  Dummy Streams, \indexit{106}
  duplicate free, 190
  `DuplicateFreeList', 195
  Duplication of Lists, \indexit{177}
  Duplication of Objects, \indexit{114}
  `DxIncludeIrreducibles', 744
\letter E
  `E', 155
  $e_N$, 159
  `EANormalSeriesByPcgs', 439
  `Earns', 401
  `EB', 159
  `EC', 159
  Echelonized Matrices, \indexit{227}
  `ED', 159
  `Edit', 74
  Editing Files, \indexit{74}
  Editor Support, \indexit{74}
  `EE', 159
  `EF', 159
  Efficiency of Homomorphisms, \indexit{382}
  `EG', 159
  `EggBoxOfDClass', 535
  `EH', 159
  `EI', 160
  `Eigenspaces', 226
  `Eigenvalues', 226
  `EigenvaluesChar', 769
  `Eigenvectors', 226
  Eigenvectors and eigenvalues, \indexit{226}
  `EJ', 160
  `EK', 160
  `EL', 160
  `ElementaryAbelianGroup', 504
  `ElementaryAbelianSeries', 365
  `ElementaryAbelianSeriesLargeSteps', 365
  Elementary Divisors, \indexit{226}
  `ElementaryDivisorsMat', 227
  `ElementaryDivisorsMatDestructive', 227
  Elementary Operations for a Pcgs, \indexit{432}
  Elementary Operations for a Pcgs and an Element, \indexit{432}
  Elementary Operations for Integers, \indexit{126}
  Elementary Operations for Rationals, \indexit{143}
  Elementary Tietze Transformations, \indexit{486}
  `ElementOfFpGroup', 460
  `ElementOfFpSemigroup', 544
  `ElementOfMagmaRing', 655
  `ElementOrdersPowerMap', 792
  `ElementProperty', 421
  `Elements', 268
  elements, definition, 110
    \sub of a list or collection, 268
  Elements as equivalence classes, \indexit{110}
  `ElementsFamily', 263
  Elements in Algebraic Extensions, \indexit{682}
  Elements of Free Magma Rings, \indexit{654}
  Elements of pc groups, \indexit{448}
  `ElementsStabChain', 419
  Elements with Prescribed Images, \indexit{396}
  element test, for lists, 179
  `elif', 51
  `EliminatedWord', 331
  `EliminationOrdering', 675
  `else', 51
  `EM', 160
  `emacs', 74
  `Embedding', 301
    \sub example for direct products, 498
    \sub example for semidirect products, 500
    \sub example for wreath products, 501
    \sub for group products, 502
    \sub for Lie algebras, 631
    \sub for magma rings, 655
  embeddings, find all, 388
  Embeddings and Projections for Group Products, \indexit{502}
  `EmptyBinaryRelation', 310
  `EmptyMatrix', 223
  `EmptySCTable', 607
  `EmptyStabChain', 420
  `EnableAttributeValueStoring', 123
  `End', 601
  `end', 55
  Enlarging Internally Represented Lists, \indexit{179}
  `Enumerator', 264
  `EnumeratorByBasis', 594
  `EnumeratorByFunctions', 264
  Enumerators, \indexit{205}
  `EnumeratorSorted', 264
  environment, 55
  `EpimorphismNilpotentQuotient', 472
  `EpimorphismPGroup', 472
  `EpimorphismQuotientSystem', 471
  epimorphisms, find all, 388
  `EpimorphismSchurCover', 376
  equality, associative words, 329
    \sub elements of finitely presented groups, 458
    \sub nonassociative words, 322
    \sub of records, 260
    \sub operation, 291
    \sub pcwords, 448
  Equality and Comparison of Domains, \indexit{283}
  equality test, 47
    \sub for permutations, 407
  equivalence class, 313
  Equivalence Classes, \indexit{313}
  `EquivalenceClasses', attribute, 314
  `EquivalenceClassOfElement', 314
  `EquivalenceClassOfElementNC', 314
  `EquivalenceClassRelation', 314
  equivalence relation, 311, 312
  `EquivalenceRelationByPairs', 313
  `EquivalenceRelationByPairsNC', 313
  `EquivalenceRelationByPartition', 313
  `EquivalenceRelationByPartitionNC', 313
  `EquivalenceRelationByProperty', 313
  `EquivalenceRelationByRelation', 313
  `EquivalenceRelationPartition', 313
  Equivalence Relations, \indexit{312}
  `ER', 160
  `Error', 72
  Error, \indexit{72}
  `ErrorCount', 72
  ErrorCount, \indexit{72}
  `ErrorNoTraceBack', 68
  errors, syntax, 64
  `ES', 160
  escaped characters, 247
  escaping non-special characters, 247
  `ET', 160
  `EU', 160
  `EuclideanDegree', 562
  `EuclideanQuotient', 562
  `EuclideanRemainder', 562
  Euclidean Rings, \indexit{562}
  Euler's totient function, 136
  `EulerianFunction', 363
  `EulerianFunctionByTom', 704
  `EV', 160
  `EvalStraightLineProgElm', 338
  `EvalString', 254
  evaluation, 42
    \sub strings, 253
  `EW', 160
  `EX', 160
  `ExactSizeConsiderFunction', 373
  `Exec', 109
  Exec, \indexit{109}
  execution, 49
  exit, 72
  expanded form of monomials, 678
  Expert Windows installation, \indexit{832}
  `Exponent', 363
    \sub for character tables, 726
  exponent, of the prime residue group, 136
  exponentiation, operation, 292
  `ExponentOfPcElement', 432
  `ExponentsConjugateLayer', 434
  `ExponentsOfCommutator', 434
  `ExponentsOfConjugate', 434
  `ExponentsOfPcElement', 432
  `ExponentsOfRelativePower', 434
  Exponents of Special Products, \indexit{434}
  `ExponentSumWord', 330
  `ExponentSyllable', 331
  Expressing Group Elements as Words in Generators, \indexit{348}
  Expressions, \indexit{42}
  `ExtendedPcgs', 436
  `ExtendStabChain', 420
  `Extension', 453
  `ExtensionNC', 453
  `ExtensionRepresentatives', 454
  `Extensions', 453
  Extensions of the p-adic Numbers, \indexit{685}
  `ExteriorPowerOfAlgebraModule', 651
  `ExternalOrbit', 404
  `ExternalOrbits', 404
  `ExternalOrbitsStabilizers', 404
  External Representation for Nonassociative Words, \indexit{325}
  external representation of polynomials, 678
  `ExternalSet', 403
  External Sets, \indexit{403}
  `ExternalSubset', 404
  `Extract', 773
  `ExtraspecialGroup', 504
  `ExtRepDenominatorRatFun', 679
  `ExtRepNumeratorRatFun', 679
  `ExtRepOfObj', external representation, for cyclotomics, 158
  `ExtRepPolynomialRatFun', 679
  `EY', 160
\letter F
  $f_N$, 159
  `FactorCosetAction', 399
    \sub for fp groups, 462
  `FactorCosetOperation', 462
  `FactorFreeSemigroupByRelations', 542
  `FactorGroup', 367
  `FactorGroupFpGroupByRels', 458
  `FactorGroupNC', 367
  `FactorGroupNormalSubgroupClasses', 754
  Factor Groups, \indexit{366}
  Factor Groups of Polycyclic Groups - Modulo Pcgs, \indexit{436}
  Factor Groups of Polycyclic Groups in their Own Representation, \indexit{438}
  `FactorGroupTom', 705
  `Factorial', 145
  `Factorization', 349
  factorization, 348
  `Factors', 562
    \sub of univariate polynomial, 667
  `FactorsInt', 132
  `FactorsOfDirectProduct', 747
  `FactorsSquarefree', 668
  Fail, \indexit{167}
  `fail', 167
  `FaithfulModule', 627
    \sub for Lie algebras, 645
  Families, \indexit{116}
  `FamiliesOfGeneralMappingsAndRanges', 309
  `FamiliesOfRows', 753
  `FamilyForOrdering', 277
  `FamilyObj', 116
  `FamilyPcgs', 447
  `FamilyRange', 309
  `FamilySource', 309
  FAQ, 824
  features, under UNIX, 27
  `fi', 51
  `Fibonacci', 153
  Fibonacci and Lucas Sequences, \indexit{153}
  `Field', 570
  `FieldExtension', 572
  field homomorphisms, Frobenius, 580
  `FieldOfMatrixGroup', 424
  `FieldOverItselfByGenerators', 571
  fields, 570
  File Access, \indexit{93}
  `FileDescriptorOfStream', 98
  `Filename', 92
  Filename, \indexit{92}
  File Operations, \indexit{94}
  File Streams, \indexit{103}
  `Filtered', 198
  Filters, \indexit{117}
  Filters Controlling the Arithmetic Behaviour of Lists, \indexit{181}
  Finding Positions in Lists, \indexit{187}
  Finding Submodules, \indexit{688}
  `FindSl2', 643
  Finish Installation and Cleanup, \indexit{823}
  Finite Field Elements, \indexit{576}
  Finitely Presented Lie Algebras, \indexit{643}
  Finitely presented monoids, \indexit{544}
  finiteness test, for a list or collection, 268
  Finite Perfect Groups, \indexit{515}
  `First', 199
  `FittingSubgroup', 358
  `Flat', 196
  flush character, 247
  For, \indexit{52}
  `ForAll', 200
  `ForAny', 200
  `for' loop, 52
  `FpElmComparisonMethod', 459
  `FpGroupPresentation', 475
  `FpGrpMonSmgOfFpGrpMonSmgElement', 542
  `FpLieAlgebraByCartanMatrix', 644
  frame, 778
  `FrattiniSubgroup', 358
    \sub for groups with pcgs, 445
  `FreeAlgebra', 606
  `FreeAlgebraWithOne', 606
  `FreeAssociativeAlgebra', 606
  `FreeAssociativeAlgebraWithOne', 606
  `FreeGeneratorsOfFpGroup', 459
  `FreeGeneratorsOfFpSemigroup', 543
  `FreeGeneratorsOfWholeGroup', 459
  `FreeGroup', 326
  `FreeGroupOfFpGroup', 459
  Free Groups, Monoids and Semigroups, \indexit{326}
  `FreeLeftModule', 568
  `FreeLieAlgebra', 632
  `FreeMagma', 324
  `FreeMagmaRing', 653
  Free Magma Rings, \indexit{653}
  Free Magmas, \indexit{324}
  `FreeMagmaWithOne', 324
  Free Modules, \indexit{567}
  `FreeMonoid', 538
    \sub with example, 327
  `FreeMonoidOfRewritingSystem', 546
  `FreeSemigroup', 327
    \sub with examples, 532
  `FreeSemigroupOfFpSemigroup', 543
  `FreeSemigroupOfRewritingSystem', 546
  Frobenius automorphism, 580
  `FrobeniusAutomorphism', 580
  FrobeniusAutomorphism, \indexit{580}
  `FrobeniusCharacterValue', 787
  `FullMatrixAlgebra', 609
  `FullMatrixAlgebraCentralizer', 617
  `FullMatrixLieAlgebra', 632
  `FullMatrixModule', 569
  `FullMatrixSpace', 598
  `FullRowModule', 569
  `FullRowSpace', 598
  `FullTransformationSemigroup', 533
  Function, \indexit{55}
  `function', 55
  `FunctionAction', 403
  function call, 46
    \sub with arguments, 46
    \sub with options, 46
  Function Calls, \indexit{46}
  `FunctionOperation', 838
  functions, 61, 299
    \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{214}
  Functions for GAP Packages, \indexit{835}
  Functions that do nothing, \indexit{62}
  Function that Modify Boolean Lists, \indexit{208}
  Function Types, \indexit{63}
  `FusionCharTableTom', 711
  `FusionConjugacyClasses', 794
  `FusionConjugacyClassesOp', 794
  fusions, 794
  `FusionsAllowedByRestrictions', 810
  `FusionsTom', 700
\letter G
  $G$-sets, 391, 403
  $g_N$, 159
  `gac', 34
  Galois Action, \indexit{572}
  Galois Conjugacy of Cyclotomics, \indexit{161}
  `GaloisCyc', 161
    \sub for class functions, 762
  `GaloisField', 579
  `GaloisGroup', of field, 573
    \sub of rational class of a group, 356
  Galois Groups of Abelian Number Fields, \indexit{586}
  `GaloisMat', 163
  `GaloisStabilizer', 584
  `GaloisType', 668
  `gap.rc', 31, 33
  GAP3, 33
  `Gap3CatalogueIdGroup', 513
  GAP for Macintosh OS X, \indexit{828}
  GAP for MacOS, \indexit{829}
  `GAPInfo', 839
  `GAPInfo.RootPaths', 29
  `GapInputPcGroup', 452
  `GapInputSCTable', 607
  `GAPKB_REW', 545
  GAP Root Directory, \indexit{90}
  `GasmanLimits', 86
  `GasmanMessageStatus', 86
  `GasmanStatistics', 86
  Gaussian algorithm, 225
  `GaussianIntegers', 588
  `GaussianRationals', 583
  Gaussians, \indexit{588}
  `Gcd', 563
  Gcd and Lcm, \indexit{563}
  `Gcdex', 130
  `GcdInt', 129
  `GcdOp', 563
  `GcdRepresentation', 563
  `GcdRepresentationOp', 563
  General Binary Relations, \indexit{310}
  `GeneralisedEigenspaces', 226
  `GeneralisedEigenvalues', 226
  generalized characters, 756
  `GeneralizedEigenspaces', 226
  `GeneralizedEigenvalues', 226
  `GeneralLinearGroup', 505
  `GeneralMappingByElements', 299
  General Mappings, \indexit{308}
  `GeneralMappingsFamily', 309
  `GeneralOrthogonalGroup', 507
  `GeneralUnitaryGroup', 506
  Generating Fields, \indexit{570}
  Generating modules, \indexit{566}
  Generating Rings, \indexit{554}
  generator, of the prime residue group, 138
  `GeneratorsOfAdditiveGroup', 552
  `GeneratorsOfAdditiveMagma', 552
  `GeneratorsOfAdditiveMagmaWithZero', 552
  `GeneratorsOfAlgebra', 613
  `GeneratorsOfAlgebraModule', 624
  `GeneratorsOfAlgebraWithOne', 613
  `GeneratorsOfDivisionRing', 571
  `GeneratorsOfDomain', 287
  `Generators\-Of\-Equivalence\-Relation\-Partition', 313
  `GeneratorsOfField', 571
  `GeneratorsOfGroup', 345
  `GeneratorsOfIdeal', 557
  `GeneratorsOfLeftIdeal', 558
  `GeneratorsOfLeftModule', 566
  `GeneratorsOfLeftOperatorAdditiveGroup', 566
  `GeneratorsOfLeftVectorSpace', 590
  `GeneratorsOfMagma', 318
  `GeneratorsOfMagmaWithInverses', 318
  `GeneratorsOfMagmaWithOne', 318
  `GeneratorsOfMonoid', 538
  `GeneratorsOfNearAdditiveGroup', 552
  `GeneratorsOfNearAdditiveMagma', 552
  `GeneratorsOfNearAdditiveMagmaWithZero', 552
  `GeneratorsOfPresentation', 475
  `GeneratorsOfRightIdeal', 558
  `GeneratorsOfRightModule', 567
  `GeneratorsOfRightOperatorAdditiveGroup', 566
  `GeneratorsOfRing', 555
  `GeneratorsOfRingWithOne', 559
  `GeneratorsOfRws', 340
  `GeneratorsOfSemigroup', 531
  `GeneratorsOf<Struct>', 284
  `GeneratorsOfTwoSidedIdeal', 557
  `GeneratorsOfVectorSpace', 590
  `GeneratorsPrimeResidues', 137
  `GeneratorsSmallest', 374
  `GeneratorsSubgroupsTom', 709
  `GeneratorSyllable', 331
  Generic Construction of Tables of Marks, \indexit{712}
  `GetFusionMap', 796
  Get the Archives, \indexit{819}
  getting help, 22
  `GF', 579
  `GL', 505
  GL and SL, \indexit{425}
  Global Memory Information, \indexit{86}
  `GModuleByMats', 687
  `GO', 507
  `GQuotients', 388
  `Grading', 618
  Green's Relations, \indexit{534}
  `GreensDClasses', 535
  `GreensDClassOfElement', 535
  `GreensDRelation', 534
  `GreensHClasses', 535
  `GreensHClassOfElement', 535
  `GreensHRelation', 534
  `GreensJClasses', 535
  `GreensJClassOfElement', 535
  `GreensJRelation', 534
  `GreensLClasses', 535
  `GreensLClassOfElement', 535
  `GreensLRelation', 534
  `GreensRClasses', 535
  `GreensRClassOfElement', 535
  `GreensRRelation', 534
  Groebner Bases, \indexit{676}
  `GroebnerBasis', 676
  `GroebnerBasisNC', 676
  `Group', 344
  group actions, 391, 392
    \sub operations syntax, 391
  Group Actions - Name Changes, \indexit{838}
  group algebra, 653
  Group Automorphisms, \indexit{384}
  `GroupByRws', 450
  `GroupByRwsNC', 450
  group characters, 756
  Group Elements, \indexit{344}
  `GroupGeneralMappingByImages', 380
  `GroupHClassOfGreensDClass', 536
  `GroupHomomorphismByFunction', 380
  `GroupHomomorphismByImages', 379
  `GroupHomomorphismByImagesNC', 379
  `GroupOfPcgs', 432
  group operations, 392, 838
  Group Properties, \indexit{361}
  `GroupRing', 653
  group ring, 653
  Groups of Automorphisms, \indexit{386}
  `GroupStabChain', 418
  `GroupWithGenerators', 345
  `GU', 506
\letter H
  $h_N$, 159
  `HallSubgroup', 359
  `HallSystem', 360
    \sub for groups with pcgs, 445
  Handling of Streams in the Background, \indexit{106}
  `HasAbelianFactorGroup', 367
  `HasElementaryAbelianFactorGroup', 367
  `HasIndeterminateName', 660
  `HasParent', 286
  `HasseDiagramBinaryRelation', 312
  `HeadPcElementByNumber', 434
  `HenselBound', 669
  hermite normal form, 838
  `HermiteNormalFormIntegerMat', 238
  `HermiteNormalFormIntegerMatTransform', 238
  `HeuristicCancelPolynomials', 681
  `HexStringInt', 250
  `HighestWeightModule', 650
  History of Character Theory Stuff in GAP, \indexit{716}
  `HMSMSec', 255
  `Hom', 601
  `HomeEnumerator', 403
  Homomorphism for very large groups, \indexit{383}
  `HomomorphismQuotientSemigroup', 534
  homomorphisms, find all, 387
  homomorphisms, Frobenius, field, 580
  Homomorphisms of Algebras, \indexit{618}
  `HomomorphismTransformationSemigroup', 533
  How to Implement New Kinds of Vector Spaces, \indexit{603}
  `HumanReadableDefinition', 707
\letter I
  $i_N$, 160
  `Ideal', 556
  `IdealByGenerators', 557
  `IdealNC', 557
  Ideals, \indexit{611}
  Ideals in Rings, \indexit{556}
  Ideals of semigroups, \indexit{533}
  `Idempotents', 319
  `IdempotentsTom', 700
  `IdempotentsTomInfo', 700
  Identical Lists, \indexit{176}
  Identical Objects, \indexit{111}
  Identical Records, \indexit{259}
  `IdentificationOfConjugacyClasses', 722
  `Identifier', for character tables, 728
    \sub for tables of marks, 701
  Identifiers, \indexit{41}
  `Identity', 288
  `IdentityBinaryRelation', 310
  `IdentityFromSCTable', 608
  `IdentityMapping', 301
  `IdentityMat', 222
  `IdentityTransformation', 547
  `IdFunc', 63
  `IdGap3SolvableGroup', 513
  `IdGroup', 513
  `IdSmallGroup', 513
  `IdsOfAllSmallGroups', 513
  If, \indexit{51}
  `if' statement, 51
  If Things Go Wrong, \indexit{824}
  `Image', 302
    \sub for Frobenius automorphisms, 580
  image, vector under matrix, 220
  `ImageElm', 302
  `ImageListOfTransformation', 547
  `Images', 303
  `ImagesElm', 302
  `ImageSetOfTransformation', 548
  `ImagesRepresentative', 302
  `ImagesSet', 302
  `ImagesSmallestGenerators', 383
  `ImagesSource', 302
  Images under Mappings, \indexit{302}
  `ImfInvariants', 526
  `ImfMatrixGroup', 527
  `ImfNumberQClasses', 524
  `ImfNumberQQClasses', 524
  `ImfNumberZClasses', 524
  `Immutable', 113
  `ImmutableBasis', 596
  `ImmutableMatrix', 232
  `in', for collections, 271
    \sub for lists, 179
    \sub for strictly sorted lists, 193
    \sub operation for, 271
  `IndependentGeneratorsOfAbelianGroup', 374
  `Indeterminate', 659
  `IndeterminateName', 660
  `Indeterminateness', 804
  `IndeterminateNumberOfLaurentPolynomial', 670
  `Indeterminate\-Number\-Of\-Univariate\-Rational\-Function', 660
  `Indeterminate\-Of\-Univariate\-Rational\-Function', 660
  Indeterminates, \indexit{659}
  `IndeterminatesOfPolynomialRing', 670
  `Index', 346
  `IndexInWholeGroup', 346
  `IndexNC', 346
  Index numbers of primitive groups, \indexit{521}
  `Indicator', 735
  `IndicatorOp', 735
  `IndicesCentralNormalSteps', 439
  `IndicesChiefNormalSteps', 440
  `IndicesEANormalSteps', 439
  `IndicesInvolutaryGenerators', 464
  `IndicesNormalSteps', 441
  `IndicesOfAdjointBasis', 614
  `IndicesPCentralNormalStepsPGroup', 440
  `IndicesStabChain', 419
  `Indirected', 800
  Induced Actions, \indexit{689}
  `InducedAutomorphism', 386
  `InducedClassFunction', 770
  `InducedClassFunctions', 770
  `InducedCyclic', 771
  `InducedPcgs', 435
  `InducedPcgsByGenerators', 435
  `InducedPcgsByGeneratorsNC', 435
  `InducedPcgsByPcSequence', 435
  `InducedPcgsByPcSequenceAndGenerators', 435
  `InducedPcgsByPcSequenceNC', 435
  `InducedPcgsWrtFamilyPcgs', 447
  `InducedPcgsWrtSpecialPcgs', 443
  `Inequalities', 787
  inequality, of records, 260
  inequality test, 47
  `InertiaSubgroup', 767
  Infinity, \indexit{158}
  `infinity', 158
  inflated class functions, 769
  `Info', 79
  `InfoAlgebra', 605
  `InfoAttributes', 123
  `InfoBckt', 421
  `InfoCharacterTable', 720
  `InfoCoh', 376
  `InfoComplement', 357
  `InfoCoset', 354
  `InfoFpGroup', 458
  Info Functions, \indexit{79}
  `InfoGroebner', 677
  `InfoGroup', 345
  `InfoLattice', 371
  `InfoLevel', 79
  `InfoMatrix', 218
  `InfoMonomial', 812
  `InfoNumtheor', 136
  `InfoOptions', 89
  `InfoPcSubgroup', 373
  Information about a function, \indexit{61}
  Information about the version used, \indexit{83}
  `InfoText', 729
  `InfoTom', 698
  `InfoWarning', 80
  `InitFusion', 809
  `InitPowerMap', 807
  `InjectionZeroMagma', 317
  `InnerAutomorphism', 385
  `InnerAutomorphismNC', 385
  `InnerAutomorphismsAutomorphismGroup', 386
  inner product, of group characters, 766
  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', 420
  `InstallAtExit', 72
  installation, 819
  Installation of GAP for MacOS, \indexit{830}
  Installation Overview, \indexit{819}
  `InstallCharReadHookFunc', 106
  `InstalledPackageVersion', 836
  `InstallFactorMaintenance', 294
  `InstallHandlingByNiceBasis', 603
  Installing a GAP Package, \indexit{834}
  `InstallIsomorphismMaintenance', 294
  `InstallSubsetMaintenance', 294
  `Int', 126
    \sub for cyclotomics, 156
    \sub for strings, 253
  `INT_CHAR', 252
  integer part of a quotient, 129
  `Integers', 126
  Integral Bases of Abelian Number Fields, \indexit{584}
  `IntegralizedMat', 241
  `IntegratedStraightLineProgram', 337
  `IntermediateGroup', 366
  `IntermediateSubgroups', 366
  Internally Represented Cyclotomics, \indexit{164}
  Internally Represented Strings, \indexit{248}
  `InterpolatedPolynomial', 565
  `IntersectBlist', 208
  `Intersection', 270
    \sub for groups with pcgs, 445
  intersection, of collections, 270
    \sub of sets, 194
  `Intersection2', 270
  `IntersectionBlist', 207
  `IntersectionsTom', 705
  `IntersectSet', 194
  `IntFFE', 578
  `IntFFESymm', 578
  `IntHexString', 253
  `IntScalarProducts', 804, 805
  `IntVecFFE', 578
  `InvariantBilinearForm', 426
  `InvariantElementaryAbelianSeries', 365
  Invariant Forms, \indexit{426}, \indexit{690}
  `InvariantLattice', 428
  `InvariantQuadraticForm', 426
  `InvariantSesquilinearForm', 426
  `Invariant\-Subgroups\-Elementary\-Abelian\-Group', 372
  `Inverse', 290
  inverse, group homomorphism, 381
    \sub matrix, 220
    \sub of class function, 761
  `InverseAttr', 290
  `InverseClasses', 729
  `InverseGeneralMapping', 300
  `InverseImmutable', 290
  `InverseMap', 799
  `InverseMatMod', 234
  `InverseMutable', 290
  `InverseOp', 290
  `InverseRepresentative', 419
  `InverseSameMutability', 290
  `InverseSM', 290
  Invoking the Help, \indexit{22}
  `Irr', 724
  irrationalities, 155
  `IrrBaumClausen', 740
  `IrrConlon', 740
  `IrrDixonSchneider', 740
  Irreducibility Tests, \indexit{688}
  irreducible character, 765
  irreducible characters, computation, 743
  `IrreducibleDifferences', 772
  Irreducible Maximal Finite Integral Matrix Groups, \indexit{522}
  `IrreducibleModules', 742
    \sub for groups with pcgs, 445
  `IrreducibleRepresentations', 741
  `IrreducibleRepresentationsDixon', 742
  `IrreducibleSolvableGroup', 522
  `IrreducibleSolvableGroupMS', 521
  Irreducible Solvable Matrix Groups, \indexit{521}
  `Is16BitsFamily', 333
  `Is32BitsFamily', 333
  `Is8BitsFamily', 333
  `IsAbelian', 319
    \sub for character tables, 726
  `IsAbelianNumberField', 583
  `IsAbelianNumberFieldPolynomialRing', 672
  `IsAbelianTom', 702
  `IsAdditiveElement', 295
  `IsAdditiveElementWithInverse', 295
  `IsAdditiveElementWithZero', 295
  `IsAdditiveGroup', 551
  `IsAdditiveGroupGeneralMapping', 307
  `IsAdditiveGroupHomomorphism', 307
  `IsAdditivelyCommutative', 552
  `IsAdditivelyCommutativeElement', 297
  `IsAdditivelyCommutativeElementCollColl', 297
  `Is\-Additively\-Commutative\-Element\-Collection', 297
  `IsAdditivelyCommutativeElementFamily', 297
  `IsAdditiveMagma', 550
  `IsAdditiveMagmaWithInverses', 551
  `IsAdditiveMagmaWithZero', 550
  `IsAlgebra', 612
  `IsAlgebraGeneralMapping', 308
  `IsAlgebraHomomorphism', 308
  `IsAlgebraicElement', 683
  `IsAlgebraicExtension', 682
  `IsAlgebraModuleElement', 624
  `IsAlgebraModuleElementCollection', 624
  `IsAlgebraModuleElementFamily', 624
  `IsAlgebraWithOne', 612
  `IsAlgebraWithOneGeneralMapping', 308
  `IsAlgebraWithOneHomomorphism', 308
  `IsAlphaChar', 249
  `IsAlternatingGroup', 412
  `IsAnticommutative', 560
  `IsAntisymmetricBinaryRelation', 311
  `IsAssociated', 560
  `IsAssociative', 319
  `IsAssociativeElement', 297
  `IsAssociativeElementCollColl', 297
  `IsAssociativeElementCollection', 297
  `IsAssocWord', 326
  `IsAssocWordWithInverse', 326
  `IsAssocWordWithOne', 326
  `IsAutomorphismGroup', 386
  `IsBasicWreathLessThanOrEqual', 329
  `IsBasicWreathProductOrdering', 281
  `IsBasis', 592
  `IsBasisByNiceBasis', 603
  `IsBasisOfAlgebraModuleElementSpace', 625
  `IsBergerCondition', 813
  `IsBijective', 302
  `IsBinaryRelation', 310
    \sub same as `IsEndoGeneralMapping', 310
  `IsBLetterAssocWordRep', 332
  `IsBLetterWordsFamily', 332
  `IsBlist', 206
  `IsBlockMatrixRep', 234
  `IsBool', 167
  `IsBound', for lists, 175
  IsBound and Unbind for Lists, \indexit{175}
  IsBound and Unbind for Records, \indexit{261}
  `IsBoundGlobal', 45
  `IsBrauerTable', 719
  `IsBravaisGroup', 428
  `IsBuiltFromAdditiveMagmaWithInverses', 341
  `IsBuiltFromGroup', 341
  `IsBuiltFromMagma', 341
  `IsBuiltFromMagmaWithInverses', 341
  `IsBuiltFromMagmaWithOne', 341
  `IsBuiltFromSemigroup', 341
  `IsCanonicalBasis', 595
  `IsCanonicalBasisFullMatrixModule', 599
  `IsCanonicalBasisFullRowModule', 599
  `IsCanonicalNiceMonomorphism', 384
  `IsCanonicalPcgs', 436
  `IsCentral', 319
  `IsChar', 245
  `IsCharacter', 765
  `IsCharacteristicSubgroup', 346
  `IsCharacterTable', 719
  `IsCharacterTableInProgress', 719
  `IsCharCollection', 245
  `IsCheapConwayPolynomial', 581
  `IsClassFunction', 756
  `IsClassFusionOfNormalSubgroup', 735
  `IsClosedStream', 97
  `IsCochain', 645
  `IsCochainCollection', 645
  `IsCollection', 263
  `IsCollectionFamily', 263
  `IsCommutative', 319
  `IsCommutativeElement', 297
  `IsCommutativeElementCollColl', 297
  `IsCommutativeElementCollection', 297
  `IsCompositionMappingRep', 300
  `IsConfluent', 339
    \sub for pc groups, 450
  `Is\-Conjugacy\-Class\-Subgroups\-By\-Stabilizer\-Rep', 368
  `IsConjugacyClassSubgroupsRep', 368
  `IsConjugate', 356
  `IsConjugatorAutomorphism', 385
  `IsConjugatorIsomorphism', 385
  `IsConstantRationalFunction', 663
  `IsConstantTimeAccessGeneralMapping', 308
  `IsConstantTimeAccessList', 171
  `IsContainedInSpan', 597
  `IsCopyable', 112
  `IsCyc', 155
  `IsCyclic', 361
    \sub for character tables, 726
  `IsCyclicTom', 702
  `IsCyclotomic', 155
  `IsCyclotomicField', 584
  `IsCyclotomicMatrixGroup', 427
  `IsDenseList', 170
  `IsDiagonalMat', 222
  `IsDigitChar', 249
  `IsDirectoryPath', 93
  `IsDistributive', 560
  `IsDivisionRing', 570
  `IsDomain', 287
  `IsDoneIterator', 274
  `IsDoubleCoset', 354
  `IsDuplicateFree', 190
  `IsDuplicateFreeList', 190
  `IsDxLargeGroup', 744
  `IsElementaryAbelian', 361
  `IsElementOfFpMonoid', 542
  `IsElementOfFpSemigroup', 542
  `IsElementOfFreeMagmaRing', 654
  `IsElementOfFreeMagmaRingCollection', 654
  `IsElementOfFreeMagmaRingFamily', 654
  `IsElementOfMagmaRingModuloRelations', 656
  `Is\-Element\-Of\-Magma\-Ring\-Modulo\-Relations\-Collection', 656
  `Is\-Element\-Of\-Magma\-Ring\-Modulo\-Relations\-Family', 656
  `Is\-Element\-Of\-Magma\-Ring\-Modulo\-Span\-Of\-Zero\-Family', 656
  `IsEmpty', 268
  `IsEmptyString', 248
  `IsEndOfStream', 100
  `IsEndoGeneralMapping', 308
    \sub same as `IsBinaryRelation', 310
  `IsEqualSet', 193
  `IsEquivalenceClass', 313
  `IsEquivalenceRelation', 311
  `IsEuclideanRing', 562
  `IsEvenInt', 127
  `IsExecutableFile', 93
  `IsExistingFile', 93
  `IsExtAElement', 295
  `IsExternalOrbit', 404
  `IsExternalSet', 403
  `IsExternalSubset', 404
  `IsExtLElement', 295
  `IsExtRElement', 295
  `IsFamilyPcgs', 447
  `IsFFE', 576
  `IsFFECollColl', 576
  `IsFFECollection', 576
  `IsField', 570
  `IsFieldControlledByGaloisGroup', 573
  `IsFieldHomomorphism', 308
  `IsFinite', 268
    \sub for character tables, 726
  `IsFiniteDimensional', 568
    \sub for matrix algebras, 613
  `IsFiniteFieldPolynomialRing', 672
  `IsFinitelyGeneratedGroup', 362
  `IsFiniteOrderElement', 297
  `IsFiniteOrderElementCollColl', 297
  `IsFiniteOrderElementCollection', 297
  `IsFiniteOrdersPcgs', 432
  `IsFixedStabilizer', 420
  `IsFLMLOR', 612
  `IsFLMLORWithOne', 612
  `IsFpGroup', 458
  `IsFpMonoid', 542
  `IsFpSemigroup', 541
  `IsFreeGroup', 327
  `IsFreeLeftModule', 567
  `IsFreeMagmaRing', 654
  `IsFreeMagmaRingWithOne', 654
  `IsFromFpGroupGeneralMappingByImages', 390
  `IsFromFpGroupHomomorphismByImages', 390
  `Is\-From\-Fp\-Group\-Std\-Gens\-General\-Mapping\-By\-Images', 390
  `Is\-From\-Fp\-Group\-Std\-Gens\-Homomorphism\-By\-Images', 390
  `IsFullHomModule', 602
  `IsFullMatrixModule', 569
  `IsFullRowModule', 569
  `Is\-Full\-Subgroup\-GLor\-SLRespecting\-Bilinear\-Form', 426
  `Is\-Full\-Subgroup\-GLor\-SLRespecting\-Quadratic\-Form', 427
  `Is\-Full\-Subgroup\-GLor\-SLRespecting\-Sesquilinear\-Form', 426
  `IsFullTransformationSemigroup', 533
  `IsFunction', 63
  `IsGaussianIntegers', 588
  `IsGaussianRationals', 583
  `IsGaussianSpace', 597
  `IsGaussInt', 158
  `IsGaussRat', 158
  `IsGeneralizedDomain', 287
  `IsGeneralizedRowVector', 181
  `IsGeneralLinearGroup', 425
  `IsGeneralMapping', 308
  `IsGeneralMappingFamily', 309
  `IsGeneratorsOf<Struct>', 284
  `IsGL', 425
  `IsGreensClass', 535
  `IsGreensDClass', 535
  `IsGreensDRelation', 534
  `IsGreensHClass', 535
  `IsGreensHRelation', 534
  `IsGreensJClass', 535
  `IsGreensJRelation', 534
  `IsGreensLClass', 535
  `IsGreensLessThanOrEqual', 535
  `IsGreensLRelation', 534
  `IsGreensRClass', 535
  `IsGreensRelation', 534
  `IsGreensRRelation', 534
  `IsGroup', 345
  `IsGroupGeneralMapping', 306
  `Is\-Group\-General\-Mapping\-By\-As\-Group\-General\-Mapping\-By\-Images', 389
  `IsGroupGeneralMappingByImages', 389
  `IsGroupGeneralMappingByPcgs', 390
  `IsGroupHClass', 536
  `IsGroupHomomorphism', 306
  `IsGroupOfAutomorphisms', 386
  `IsGroupRing', 654
  `IsHandledByNiceBasis', 569
    \sub for vector spaces, 603
  `IsHandledByNiceMonomorphism', 384
  `IsHasseDiagram', 311
  `IsHomogeneousList', 171
  `IsIdempotent', 290
  `IsIdenticalObj', 111
  `IsIncomparableUnder', 277
  `IsInducedFromNormalSubgroup', 815
  `IsInducedPcgs', 435
  `IsInducedPcgsWrtSpecialPcgs', 443
  `IsInfBitsFamily', 333
  `IsInfinity', 158
  `IsInjective', 301
  `IsInnerAutomorphism', 385
  `IsInputOutputStream', 104
  `IsInputStream', 97
  `IsInputTextNone', 97
  `IsInputTextStream', 97
  `IsInt', 126
  `IsIntegerMatrixGroup', 427
  `IsIntegers', 126
  `IsIntegralBasis', 595
  `IsIntegralCyclotomic', 156
  `IsIntegralRing', 559
  `IsInternallyConsistent', 115
    \sub for character tables, 734
    \sub for tables of marks, 702
  `IsIrreducibleCharacter', 765
  `IsIrreducibleRingElement', 561
  `IsIterator', 274
  `IsJacobianElement', 297
  `IsJacobianElementCollColl', 297
  `IsJacobianElementCollection', 297
  `IsJacobianRing', 560
  `IsLaurentPolynomial', 663
  `IsLaurentPolynomialDefaultRep', 679
  `IsLDistributive', 559
  `IsLeftAlgebraModuleElement', 624
  `IsLeftAlgebraModuleElementCollection', 624
  `IsLeftIdeal', 557
  `IsLeftIdealInParent', 557
  `IsLeftModule', 566
  `IsLeftModuleGeneralMapping', 307
  `IsLeftModuleHomomorphism', 307
  `IsLeftOperatorAdditiveGroup', 566
  `IsLeftSemigroupIdeal', 533
  `IsLeftVectorSpace', 589
  `IsLessThanOrEqualUnder', 277
  `IsLessThanUnder', 277
  `IsLetterAssocWordRep', 332
  `IsLetterWordsFamily', 332
  `IsLexicographicallyLess', 196
  `IsLieAbelian', 635
  `IsLieAlgebra', 612
  `IsLieMatrix', 219
  `IsLieNilpotent', 635
  `IsLieObject', 630
  `IsLieObjectCollection', 630
  `IsLieSolvable', 635
  `IsLinearMapping', 307
  `IsLinearMappingsModule', 602
  `IsList', 170
  `IsListDefault', 181
  `IsListOrCollection', 264
  `IsLowerAlphaChar', 249
  `IsLowerTriangularMat', 222
  `IsMagma', 315
  `IsMagmaHomomorphism', 305
  `IsMagmaRingModuloRelations', 656
  `IsMagmaRingModuloSpanOfZero', 656
  `IsMagmaWithInverses', 315
  `IsMagmaWithInversesIfNonzero', 315
  `IsMagmaWithOne', 315
  `IsMapping', 301
  `IsMatchingSublist', 190
  `IsMatrix', 218
  `IsMatrixGroup', 424
  `IsMatrixModule', 569
  `IsMatrixSpace', 597
  `IsMinimalNonmonomial', 818
  `IsModuloPcgs', 437
  `IsMonoid', 538
  `IsMonomial', for characters, 815
    \sub for character tables, 726
    \sub for groups, 815
    \sub for positive integers, 816
  `IsMonomialGroup', 361
  `IsMonomialMatrix', 222
  `IsMonomialNumber', 816
  `IsMonomialOrdering', 672
  `IsMultiplicativeElement', 295
  `IsMultiplicativeElementWithInverse', 296
  `IsMultiplicativeElementWithOne', 295
  `IsMultiplicativeElementWithZero', 295
  `IsMultiplicativeGeneralizedRowVector', 181
  `IsMultiplicativeZero', 319
  `IsMutable', 113
  `IsMutableBasis', 596
  `IsNaturalAlternatingGroup', 411
  `IsNaturalGL', 425
  `IsNaturalGLnZ', 427
  `IsNaturalSL', 426
  `IsNaturalSLnZ', 428
  `IsNaturalSymmetricGroup', 411
  `IsNearAdditiveElement', 295
  `IsNearAdditiveElementWithInverse', 295
  `IsNearAdditiveElementWithZero', 295
  `IsNearAdditiveGroup', 550
  `IsNearAdditiveMagma', 550
  `IsNearAdditiveMagmaWithInverses', 550
  `IsNearAdditiveMagmaWithZero', 550
  `IsNearlyCharacterTable', 719
  `IsNearRingElement', 296
  `IsNearRingElementWithInverse', 296
  `IsNearRingElementWithOne', 296
  `IsNegRat', 144
  `IsNilpotent', for character tables, 726
    \sub for groups with pcgs, 445
  `IsNilpotentElement', 642
  `IsNilpotentGroup', 361
  `IsNilpotentTom', 702
  `IsNonassocWord', 322
  `IsNonassocWordCollection', 322
  `IsNonassocWordWithOne', 322
  `IsNonassocWordWithOneCollection', 322
  `IsNonnegativeIntegers', 126
  `IsNonSPGeneralMapping', 309
  `IsNonTrivial', 268
  `IsNormal', 346
  `IsNormalBasis', 595
  `IsNotIdenticalObj', 112
  `IsNumberField', 583
  `IsObject', 110
  `IsOddInt', 127
  isomorphic, pc group, 451, 452
  `IsomorphicSubgroups', 388
  `IsomorphismFpAlgebra', 621
  `IsomorphismFpGroup', 466
    \sub for subgroups of fp groups, 469
  `IsomorphismFpGroupByGenerators', 467
  `IsomorphismFpGroupByGeneratorsNC', 467
  `IsomorphismFpGroupByPcgs', 449
  `IsomorphismFpSemigroup', 542
  `IsomorphismGroups', 387
  `IsomorphismMatrixAlgebra', 621
  `IsomorphismPcGroup', 452
  `IsomorphismPermGroup', 410
    \sub for Imf matrix groups, 529
  `IsomorphismPermGroupImfGroup', 530
  `IsomorphismReesMatrixSemigroup', 537
  `IsomorphismRefinedPcGroup', 451
  `Isomorphism<Rep><Struct>', 285
  isomorphisms, find all, 388
  `IsomorphismSCAlgebra', 622
  `IsomorphismSimplifiedFpGroup', 469
  `IsomorphismSpecialPcGroup', 452
  `IsomorphismTransformationSemigroup', 533
  `IsomorphismTypeInfoFiniteSimpleGroup', 361
  `IsOne', 290
  `IsOperation', 63
  `IsOrdering', 276
  `IsOrderingOnFamilyOfAssocWords', 277
  `IsOrdinaryMatrix', 218
  `IsOrdinaryTable', 719
  `IsOutputStream', 97
  `IsOutputTextNone', 98
  `IsOutputTextStream', 97
  `IsPadicExtensionNumber', 685
  `IsPadicExtensionNumberFamily', 685
  `IsParentPcgsFamilyPcgs', 447
  `IsPartialOrderBinaryRelation', 311
  `IsPcGroup', 448
  `IsPcGroupGeneralMappingByImages', 390
  `IsPcGroupHomomorphismByImages', 390
  `IsPcgs', 431
  `IsPcgsCentralSeries', 439
  `IsPcgsChiefSeries', 440
  `IsPcgsElementaryAbelianSeries', 439
  `IsPcgsPCentralSeriesPGroup', 440
  `IsPerfect', for character tables, 726
  `IsPerfectGroup', 361
  `IsPerfectTom', 702
  `IsPerm', 406
  `IsPermCollColl', 406
  `IsPermCollection', 406
  `IsPermGroup', 410
  `IsPermGroupGeneralMappingByImages', 390
  `IsPermGroupHomomorphismByImages', 390
  `IsPGroup', 362
  `IsPNilpotent', 363
  `IsPolycyclicGroup', 361
  `IsPolynomial', 663
  `IsPolynomialDefaultRep', 679
  `IsPolynomialFunction', 662
  `IsPolynomialFunctionsFamily', 677
  `IsPolynomialRing', 671
  `IsPosInt', 126
  `IsPositiveIntegers', 126
  `IsPosRat', 143
  `Is\-Preimages\-By\-As\-Group\-General\-Mapping\-By\-Images', 390
  `IsPreOrderBinaryRelation', 311
  `IsPrime', 561
  `IsPrimeField', 572
  `IsPrimeInt', 131
  `IsPrimeOrdersPcgs', 432
  `IsPrimePowerInt', 132
  `IsPrimitive', 401
  `IsPrimitiveCharacter', 814
  `IsPrimitivePolynomial', 664
  `IsPrimitiveRootMod', 138
  `IsProbablyPrimeInt', 131
  `IsPseudoCanonicalBasisFullHomModule', 602
  `IsPSolvable', 363
  `IsPSolvableCharacterTable', 735
  `IsPSolvableCharacterTableOp', 735
  `IsPurePadicNumber', 684
  `IsPurePadicNumberFamily', 684
  `IsQuasiPrimitive', 814
  `IsQuaternion', 613
  `IsQuaternionCollColl', 613
  `IsQuaternionCollection', 613
  `IsQuickPositionList', 205
  `IsQuotientSemigroup', 534
  `IsRange', 204
  `IsRat', 143
  `IsRationalFunction', 662
  `IsRationalFunctionDefaultRep', 678
  `IsRationalFunctionsFamily', 677
  `IsRationalMatrixGroup', 427
  `IsRationals', 143
  `IsRationalsPolynomialRing', 672
  `IsRDistributive', 560
  `IsReadableFile', 93
  `IsReadOnlyGlobal', 44
  `IsRecord', 257
  `IsRecordCollColl', 257
  `IsRecordCollection', 257
  `IsReduced', 340
  `IsReductionOrdering', 278
  `IsReesCongruence', 534
  `IsReesCongruenceSemigroup', 532
  `IsReesMatrixSemigroup', 536
  `IsReesMatrixSemigroupElement', 536
  `IsReesZeroMatrixSemigroup', 536
  `IsReesZeroMatrixSemigroupElement', 536
  `IsReflexiveBinaryRelation', 310
  `IsRegular', 401
  `IsRegularDClass', 536
  `IsRegularSemigroup', 532
  `IsRegularSemigroupElement', 532
  `IsRelativelySM', 817
  `IsRestrictedLieAlgebra', 640
  `IsRewritingSystem', 339
  `IsRightAlgebraModuleElement', 624
  `IsRightAlgebraModuleElementCollection', 624
  `IsRightCoset', 352
  `IsRightIdeal', 557
  `IsRightIdealInParent', 557
  `IsRightModule', 566
  `IsRightOperatorAdditiveGroup', 566
  `IsRightSemigroupIdeal', 533
  `IsRing', 554
  `IsRingElement', 296
  `IsRingElementWithInverse', 296
  `IsRingElementWithOne', 296
  `IsRingGeneralMapping', 308
  `IsRingHomomorphism', 308
  `IsRingWithOne', 558
  `IsRingWithOneGeneralMapping', 308
  `IsRingWithOneHomomorphism', 308
  `IsRootSystem', 636
  `IsRootSystemFromLieAlgebra', 637
  `IsRowModule', 569
  `IsRowSpace', 597
  `IsRowVector', 210
  `IsScalar', 296
  `IsSemiEchelonized', 598
  `IsSemigroup', 531
  `IsSemigroupCongruence', 533
  `IsSemigroupIdeal', 533
  `IsSemiRegular', 401
  `IsSet', 191
  `IsShortLexLessThanOrEqual', 329
  `IsShortLexOrdering', 279
  `IsSimple', for character tables, 726
  `IsSimpleAlgebra', 612
  `IsSimpleGroup', 361
  `IsSimpleSemigroup', 532
  `IsSingleValued', 301
  `IsSL', 425
  `IsSolvable', for character tables, 726
  `IsSolvableGroup', 361
  `IsSolvableTom', 702
  `IsSortedList', 190
  `IsSpecialLinearGroup', 425
  `IsSpecialPcgs', 442
  `IsSPGeneralMapping', 309
  `IsSporadicSimple', for character tables, 726
  `IsSSortedList', 191
  `IsStandardGeneratorsOfGroup', 708
  `IsStraightLineProgElm', 338
  `IsStraightLineProgram', 334
  `IsStream', 97
  `IsString', 245
  `IsStringRep', 248
  `Is<Struct>', 285
  `IsSubgroup', 346
  `IsSubgroupFpGroup', 458
  `IsSubgroupOfWholeGroupByQuotientRep', 470
  `IsSubgroupSL', 426
  `IsSubmonoidFpMonoid', 541
  `IsSubnormal', 347
  `IsSubnormallyMonomial', 817
  `IsSubsemigroupFpSemigroup', 541
  `IsSubset', 270
  `IsSubsetBlist', 207
  `IsSubsetLocallyFiniteGroup', 362
  `IsSubsetSet', 193
  `IsSubspacesVectorSpace', 590
  `IsSub<struct>', 287
  `IsSupersolvable', for character tables, 726
    \sub for groups with pcgs, 445
  `IsSupersolvableGroup', 361
  `IsSurjective', 302
  `IsSyllableAssocWordRep', 333
  `IsSyllableWordsFamily', 333
  `IsSymmetricBinaryRelation', 310
  `IsSymmetricGroup', 412
  `IsTable', 171
  `IsTableOfMarks', 698
  `IsTableOfMarksWithGens', 709
  `IsToPcGroupGeneralMappingByImages', 390
  `IsToPcGroupHomomorphismByImages', 390
  `IsToPermGroupGeneralMappingByImages', 390
  `IsToPermGroupHomomorphismByImages', 390
  `IsTotal', 301
  `IsTotalOrdering', 277
  `IsTransformation', 547
  `IsTransformationCollection', 547
  `IsTransformationMonoid', 533
  `IsTransformationSemigroup', 533
  `IsTransitive', for characters, 768
    \sub for class functions, 768
    \sub for group actions, 400
  `IsTransitiveBinaryRelation', 310
  `IsTranslationInvariantOrdering', 277
  `IsTrivial', 268
  `IsTuple', 299
  `IsTwoSidedIdeal', 557
  `IsTwoSidedIdealInParent', 557
  `IsUEALatticeElement', 648
  `IsUEALatticeElementCollection', 648
  `IsUEALatticeElementFamily', 648
  `IsUniqueFactorizationRing', 559
  `IsUnit', 560
  `IsUnivariatePolynomial', 663
  `IsUnivariatePolynomialRing', 672
  `IsUnivariateRationalFunction', 663
  `IsUnknown', 165
  `IsUpperAlphaChar', 249
  `IsUpperTriangularMat', 222
  `IsValidIdentifier', 42
  `IsVector', 296
  `IsVectorSpace', 589
  `IsVirtualCharacter', 765
  `IsWeightLexOrdering', 280
  `IsWeightRepElement', 649
  `IsWeightRepElementCollection', 649
  `IsWeightRepElementFamily', 649
  `IsWellFoundedOrdering', 276
  `IsWeylGroup', 638
  `IsWholeFamily', 269
  `IsWLetterAssocWordRep', 332
  `IsWLetterWordsFamily', 332
  `IsWord', 321
  `IsWordCollection', 322
  `IsWordWithInverse', 321
  `IsWordWithOne', 321
  `IsWreathProductOrdering', 281
  `IsWritableFile', 93
  `IsZero', 290
  `IsZeroGroup', 532
  `IsZeroSimpleSemigroup', 532
  `IsZeroSquaredElement', 297
  `IsZeroSquaredElementCollColl', 297
  `IsZeroSquaredElementCollection', 297
  `IsZeroSquaredRing', 560
  `IsZmodnZObj', 134
  `IsZmodnZObjNonprime', 134
  `IsZmodpZObj', 134
  `IsZmodpZObjLarge', 134
  `IsZmodpZObjSmall', 134
  `Iterated', 201
  `Iterator', 273
  `IteratorByBasis', 594
  `IteratorByFunctions', 275
  `IteratorList', 274
  Iterators, \indexit{273}
  `IteratorSorted', 274
\letter J
  $j_N$, 160
  `Jacobi', 138
  `JenningsLieAlgebra', 641
  `JenningsSeries', 366
  `JoinEquivalenceRelations', 313
  `JoinStringsWithSeparator', 251
  `JordanDecomposition', 230
\letter K
  $k_N$, 160
  `KappaPerp', 642
  `KB_REW', 545
  `KernelOfAdditiveGeneralMapping', 307
  `KernelOfCharacter', 767
  `KernelOfMultiplicativeGeneralMapping', 306
  `KernelOfTransformation', 548
  Keywords, \indexit{41}
  `KillingMatrix', 642
  `KnownAttributesOfObject', 121
  Known Problems of the Configure Process, \indexit{826}
  `KnownPropertiesOfObject', 124
  `KnownTruePropertiesOfObject', 124
  `KnowsHowToDecompose', 378
  `KnuthBendixRewritingSystem', 545
  Krasner-Kaloujnine theorem, 502
  `KroneckerProduct', 224
  `KuKGenerators', 502
\letter L
  $l_N$, 160
  `Lambda', 136
  Language Overview, \indexit{39}
  larger or equal, 47
  larger test, 47
  `LargestElementGroup', 374
  `LargestElementStabChain', 419
  `LargestMovedPoint', 407
  `LargestUnknown', 165
  `last', 64
  `LastSystemError', 90
  `LaTeXStringDecompositionMatrix', 733
  lattice base reduction, 241, 242
  lattice basis reduction, for virtual characters, 772
  `LatticeByCyclicExtension', 371
  `LatticeGeneratorsInUEA', 648
  Lattice Reduction, \indexit{241}
  `LatticeSubgroups', 369
  `LatticeSubgroupsByTom', 695
  `LaurentPolynomialByCoefficients', 669
  `LaurentPolynomialByExtRep', 680
  Laurent Polynomials, \indexit{669}
  `LClassOfHClass', 535
  `Lcm', 564
  `LcmInt', 130
  `LcmOp', 564
  `LeadCoeffsIGS', 436
  `LeadingCoefficient', 665
  `LeadingCoefficientOfPolynomial', 673
  `LeadingExponentOfPcElement', 433
  `LeadingMonomial', 665
  `LeadingMonomialOfPolynomial', 673
  `LeadingTermOfPolynomial', 673
  Leaving GAP, \indexit{72}
  `LeftActingAlgebra', 625
  `LeftActingDomain', 567
  `LeftActingRingOfIdeal', 558
  `LeftAlgebraModule', 623
  `LeftAlgebraModuleByGenerators', 622
  left cosets, 352
  `LeftDerivations', 632
  `LeftIdeal', 556
  `LeftIdealByGenerators', 557
  `LeftIdealNC', 557
  `LeftModuleByGenerators', 567
  `LeftModuleByHomomorphismToMatAlg', 626
  `LeftModuleGeneralMappingByImages', 600
  `LeftModuleHomomorphismByImages', 600
  `LeftModuleHomomorphismByImagesNC', 600
  `LeftModuleHomomorphismByMatrix', 601
  `LeftQuotient', 292
    \sub for words, 329
  `LeftShiftRowVector', 214
  legacy, 838
  `Legendre', 139
  `Length', 191
    \sub of an associative word, 330
  length, of a word, 330
  `LengthsTom', 699
  `LenstraBase', 586
  `LessThanFunction', 277
  `LessThanOrEqualFunction', 277
  `LetterRepAssocWord', 333
  `LevelsOfGenerators', 281
  `LeviMalcevDecomposition', 618
    \sub for Lie algebras, 636
  Lexical Structure, \indexit{40}
  `LexicographicOrdering', 278
  `LGFirst', 443
  `LGLayers', 442
  `LGLength', 443
  `LGWeights', 442
  library tables, 717
  `LieAlgebra', 631
  `LieAlgebraByStructureConstants', 631
  `LieBracket', 292
  `LieCenter', 633
  `LieCentralizer', 633
  `LieCentre', 633
  `LieCoboundaryOperator', 646
  `LieDerivedSeries', 634
  `LieDerivedSubalgebra', 633
  `LieFamily', 630
  `LieLowerCentralSeries', 634
  `LieNilRadical', 634
  `LieNormalizer', 633
  `LieObject', 630
  Lie objects, \indexit{630}
  `LieSolvableRadical', 634
  `LieUpperCentralSeries', 635
  `LiftedInducedPcgs', 438
  `LiftedPcElement', 438
  `LinearAction', 444
  `LinearActionLayer', 444
  `LinearCharacters', 725
  `LinearCombination', 594
  `LinearCombinationPcgs', 433
  Linear equations over the integers and Integral Matrices, \indexit{236}
  `LinearIndependentColumns', 240
  Linear Mappings, \indexit{307}
  `LinearOperation', 444
  `LinearOperationLayer', 444
  Line Editing, \indexit{73}
  `LinesOfStraightLineProgram', 335
  `List', 198
  list and non-list, difference, 183
    \sub left quotient, 186
    \sub mod, 185
    \sub product, 184
    \sub quotient, 185
  List Assignment, \indexit{173}
  list assignment, operation, 172
  `ListBlist', 206
  list boundedness test, operation, 172
  List Categories, \indexit{170}
  list element, access, 172
    \sub assignment, 173
    \sub operation, 172
  List Elements, \indexit{172}
  list equal, comparison, 179
  `ListN', 201
  list of available books, 23
  `ListPerm', 408
  Lists and Collections, \indexit{264}
  list smaller, comparison, 180
  `ListStabChain', 419
  list unbind, operation, 172
  `ListWithIdenticalEntries', 187
  `ListX', 202
  `LLL', 772
  LLL algorithm, for Gram matrices, 242
    \sub for vectors, 241
    \sub for virtual characters, 772
  `LLLReducedBasis', 241
  `LLLReducedGramMat', 242
  `LoadDynamicModule', 35
  Loading a GAP Package, \indexit{834}
  loading a saved workspace, 37
  `LoadPackage', 834
  `local', 55
  logarithm, discrete, 137
    \sub of a root of unity, 158
  `LogFFE', 578
  logical, 167
  logical operations, 168
  `LogInt', 128
  `LogMod', 137
  `LogModShanks', 137
  `LogTo', 95
    \sub for streams, 102
    \sub stop logging, 95
  `LongestWeylWordPerm', 639
  loop, read eval print, 64
  loop, `for', 52
    \sub `repeat', 52
    \sub `while', 51
  loop over iterator, 54
  loop over object, 54
  loop over range, 53
  loops, leaving, 54
    \sub restarting, 55
  `LowercaseString', 250
  `LowerCentralSeriesOfGroup', 365
  Low Index Subgroups, \indexit{465}
  `LowIndexSubgroupsFpGroup', 465
  Low Level Routines to Modify and Create Stabilizer Chains, \indexit{419}
  `Lucas', 153
\letter M
  $m_N$, 160
  Macintosh, 828, 829
  MacOS, 829
  `Magma', 315
  `MagmaByGenerators', 316
  `MagmaByMultiplicationTable', 317
  Magma Categories, \indexit{315}
  `MagmaElement', 317
  Magma Generation, \indexit{315}
  `MagmaHomomorphismByFunctionNC', 305
  Magma Homomorphisms, \indexit{305}
  `MagmaRingModuloSpanOfZero', 656
  Magma Rings modulo Relations, \indexit{656}
  Magma Rings modulo the Span of a Zero Element, \indexit{656}
  Magmas Defined by Multiplication Tables, \indexit{317}
  `MagmaWithInverses', 316
  `MagmaWithInversesByGenerators', 316
  `MagmaWithInversesByMultiplicationTable', 317
  `MagmaWithOne', 315
  `MagmaWithOneByGenerators', 316
  `MagmaWithOneByMultiplicationTable', 317
  Main Loop, \indexit{64}
  `MakeConfluent', 340
  `MakeImmutable', 113
  `MakeReadOnlyGlobal', 44
  `MakeReadWriteGlobal', 44
  Making transformation semigroups, \indexit{533}
  Manual Conventions, \indexit{20}
  map, parametrized, 799
  `MappedWord', 323
  `MappingByFunction', 299
  `MappingPermListList', 409
  Mappings that Respect Addition, \indexit{306}
  Mappings that Respect Multiplication, \indexit{305}
  Mappings which are Compatible with Algebraic Structures, \indexit{305}
  maps, 790
  `MarksTom', 698
  `MatAlgebra', 609
  `MatClassMultCoeffsCharTable', 737
  `MathieuGroup', 505
  `MatLieAlgebra', 632
  matrices, commutator, 220
  Matrices as Basis of a Row Space, \indexit{228}
  Matrices as Linear Mappings, \indexit{230}
  Matrices over Finite Fields, \indexit{231}
  Matrices Representing Linear Equations and the Gaussian Algorithm, \indexit{225}
  `MatrixAlgebra', 609
  `MatrixAutomorphisms', 751
  matrix automorphisms, 793
  `MatrixByBlockMatrix', 235
  Matrix Constructions, \indexit{222}
  Matrix Groups in Characteristic 0, \indexit{427}
  `MatrixLieAlgebra', 632
  `MatrixOfAction', 625
  matrix spaces, 597
  `MatScalarProducts', 766
  `MatTom', 701
  `MaximalAbelianQuotient', 367
  `MaximalBlocks', 402
  `MaximalNormalSubgroups', 369
  `MaximalSubgroupClassReps', 368
  `MaximalSubgroups', 368
    \sub for groups with pcgs, 445
  `MaximalSubgroupsLattice', 369
  `MaximalSubgroupsTom', 705
  `Maximum', 197
  `MaximumList', 197
  MeatAxe Modules, \indexit{687}
  `MeetEquivalenceRelations', 313
  `MeetMaps', 802
  Membership Test for Collections, \indexit{271}
  Membership Test for Lists, \indexit{179}
  `MinimalElementCosetStabChain', 419
  `MinimalGeneratingSet', 374
    \sub for groups with pcgs, 445
  `MinimalNonmonomialGroup', 818
  Minimal Nonmonomial Groups, \indexit{818}
  `MinimalNormalSubgroups', 369
  `MinimalPolynomial', 667
    \sub over a field, 573
    \sub over a ring, 667
  Minimal Polynomials, \indexit{667}
  `MinimalStabChain', 417
  `MinimalSupergroupsLattice', 370
  `MinimalSupergroupsTom', 706
  `MinimizedBombieriNorm', 669
  `Minimum', 197
  `MinimumList', 197
  `MinusCharacter', 808
  Miscellaneous, \indexit{142}
  Miscellaneous Name Changes or Removed Names, \indexit{839}
  mod, integers, 134
    \sub laurent polynomials, 661
    \sub lists, 185
    \sub rationals, 48
  `mod', 48
    \sub arithmetic operators, 48
    \sub for character tables, 723
    \sub residue class rings, 133
  modular inverse, 48
  modular remainder, 48
  modular roots, 140
  `ModuleByRestriction', 627
  Module Constructions, \indexit{687}
  Module Homomorphisms, \indexit{689}
  `ModuleOfExtension', 453
  Modules over Lie Algebras and Their Cohomology, \indexit{645}
  Modules over Semisimple Lie Algebras, \indexit{647}
  modulo, 48
    \sub arithmetic operators, 48
    \sub for pcgs, 437
    \sub residue class rings, 133
  `ModuloPcgs', 437
  `MoebiusMu', 141
  `MoebiusTom', 701
  Molien Series, \indexit{779}
  `MolienSeries', 779
  `MolienSeriesInfo', 780
  `MolienSeriesWithGivenDenominator', 781
  `Monoid', 538
  `MonoidByGenerators', 538
  `MonoidByMultiplicationTable', 539
  `MonoidOfRewritingSystem', 546
  `MonomialComparisonFunction', 673
  `MonomialExtGrlexLess', 675
  `MonomialExtrepComparisonFun', 674
  `MonomialGrevlexOrdering', 674
  `MonomialGrlexOrdering', 674
  `MonomialLexOrdering', 674
  Monomial Orderings, \indexit{672}
  `MonomialTotalDegreeLess', 839
  monomorphisms, find all, 388
  `MorClassLoop', 388
  More about Boolean Lists, \indexit{208}
  More About Global Variables, \indexit{44}
  More about Tables of Marks, \indexit{693}
  `MostFrequentGeneratorFpGroup', 464
  `MovedPoints', 407
  Moved Points of Permutations, \indexit{407}
  `MTX.BasesCompositionSeries', 689
  `MTX.BasesMaximalSubmodules', 688
  `MTX.BasesMinimalSubmodules', 688
  `MTX.BasesMinimalSupermodules', 689
  `MTX.BasesSubmodules', 688
  `MTX.BasisInOrbit', 690
  `MTX.BasisRadical', 688
  `MTX.BasisSocle', 688
  `MTX.CollectedFactors', 689
  `MTX.CompositionFactors', 689
  `MTX.DegreeSplittingField', 688
  `MTX.Dimension', 688
  `MTX.Distinguish', 690
  `MTX.Field', 688
  `MTX.Generators', 688
  `MTX.Homomorphism', 690
  `MTX.Homomorphisms', 690
  `MTX.InducedAction', 689
  `MTX.InducedActionFactorMatrix', 689
  `MTX.InducedActionFactorModule', 689
  `MTX.InducedActionMatrix', 689
  `MTX.InducedActionMatrixNB', 689
  `MTX.InducedActionSubmodule', 689
  `MTX.InducedActionSubmoduleNB', 689
  `MTX.InvariantBilinearForm', 690
  `MTX.InvariantQuadraticForm', 690
  `MTX.InvariantSesquilinearForm', 690
  `MTX.IsAbsolutelyIrreducible', 688
  `MTX.IsEquivalent', 689
  `MTX.IsIrreducible', 688
  `MTX.Isomorphism', 690
  `MTX.NormedBasisAndBaseChange', 689
  `MTX.OrthogonalSign', 690
  `MTX.ProperSubmoduleBasis', 688
  `MTX.SubGModule', 688
  `MTX.SubmoduleGModule', 688
  multiplication, 48
    \sub matrices, 220
    \sub matrix and matrix list, 221
    \sub matrix and scalar, 219
    \sub matrix and vector, 220
    \sub operation, 292
    \sub scalar and matrix, 219
    \sub scalar and matrix list, 220
    \sub scalar and vector, 211
    \sub vector and matrix, 219
    \sub vector and matrix list, 221
    \sub vector and scalar, 211
    \sub vectors, 211
  `MultiplicationTable', 317
  Multiplicative Arithmetic for Lists, \indexit{184}
  Multiplicative Arithmetic Functions, \indexit{140}
  `MultiplicativeNeutralElement', 319
  multiplicative order of an integer, 137
  `MultiplicativeZero', 319
  `MultiplicativeZeroOp', 289
  multiplicity, of constituents of a group character, 766
  multiplier, 377
  multisets, 192
  Multivariate Polynomials, \indexit{666}
  `MultRowVector', 214
  Murnaghan components, 778, 779
  Mutability and Copyability, \indexit{112}
  Mutability Status and List Arithmetic, \indexit{186}
  Mutable Bases, \indexit{595}
  `MutableBasis', 596
  `MutableBasisOfClosureUnderAction', 615
  `Mutable\-Basis\-Of\-Ideal\-In\-Nonassociative\-Algebra', 616
  `MutableBasisOfNonassociativeAlgebra', 616
  `MutableIdentityMat', 224
  `MutableNullMat', 224
\letter N
  $n_k$, 160
  `Name', 115
  `NameFunction', 61
  `NameRNam', 262
  `NamesFilter', 118
  `NamesGVars', 45
  `NamesLocalVariablesFunction', 61
  `NamesOfFusionSources', 797
  `NamesSystemGVars', 45
  `NamesUserGVars', 45
  `NaturalCharacter', 764
  Natural Embeddings related to Magma Rings, \indexit{655}
  `NaturalHomomorphismByGenerators', 305
  `NaturalHomomorphismByIdeal', 620
  `NaturalHomomorphismByNormalSubgroup', 366
  `NaturalHomomorphismByNormalSubgroupNC', 366
  `NaturalHomomorphismBySubAlgebraModule', 627
  `NaturalHomomorphismBySubspace', 601
  `NearAdditiveGroup', 551
  `NearAdditiveGroupByGenerators', 551
  `NearAdditiveMagma', 551
  `NearAdditiveMagmaByGenerators', 551
  `NearAdditiveMagmaWithZero', 551
  `NearAdditiveMagmaWithZeroByGenerators', 551
  `NearlyCharacterTablesFamily', 721
  negative number, 48
  `NegativeRoots', 637
  `NegativeRootVectors', 637
  `NestingDepthA', 182
  `NestingDepthM', 182
  `NewInfoClass', 79
  newline, 40
  newline character, 247
  `NewmanInfinityCriterion', 474
  New Presentations and Presentations for Subgroups, \indexit{469}
  `NextIterator', 274
  `NextPrimeInt', 132
  `NF', 582
  `NiceBasis', 603
  `NiceBasisFiltersInfo', 604
  `NiceFreeLeftModule', 602
  `NiceFreeLeftModuleInfo', 603
  `NiceMonomorphism', 384
  `NiceMonomorphismAutomGroup', 387
  Nice Monomorphisms, \indexit{383}
  `NiceObject', 384
  `NiceVector', 602
  `NilpotencyClassOfGroup', 361
  `NilpotentQuotientOfFpLieAlgebra', 644
  `NK', 160
  `NOAUTO', 835
  `NonnegativeIntegers', 126
  `NonnegIntScalarProducts', 804, 805
  `NonNilpotentElement', 642
  `Norm', 573
    \sub of character, 766
  `NormalBase', 574
  `NormalClosure', 356
  `NormalFormIntMat', 239
  Normal Forms of Integer Matrices - Name Changes, \indexit{838}
  Normal Forms over the Integers, \indexit{237}
  `NormalIntersection', 357
  `Normalized\-Element\-Of\-Magma\-Ring\-Modulo\-Relations', 656
  `NormalizedWhitespace', 251
  `Normalizer', 356
  normalizer, 356
  `NormalizerInGLnZ', 428
  `NormalizerInGLnZBravaisGroup', 428
  `NormalizersTom', 703
  `NormalizerTom', 703
  `NormalizeWhitespace', 251
  `NormalSeriesByPcgs', 441
  Normal Structure, \indexit{356}
  `NormalSubgroupClasses', 754
  `NormalSubgroupClassesInfo', 753
  `NormalSubgroups', 369
  `NormedRowVector', 212
  `NormedRowVectors', 599
  `NormedVectors', 839
  `not', 169
  `NrArrangements', 147
  `NrBasisVectors', 596
  `NrCombinations', 147
  `NrConjugacyClasses', 355
    \sub for character tables, 726
  `NrConjugacyClassesGL', 509
  `NrConjugacyClassesGU', 509
  `NrConjugacyClassesPGL', 509
  `NrConjugacyClassesPGU', 509
  `NrConjugacyClassesPSL', 509
  `NrConjugacyClassesPSU', 509
  `NrConjugacyClassesSL', 509
  `NrConjugacyClassesSLIsogeneous', 509
  `NrConjugacyClassesSU', 509
  `NrConjugacyClassesSUIsogeneous', 509
  `NrDerangements', 150
  `NrInputsOfStraightLineProgram', 335
  `NrMovedPoints', 407
  `NrOrderedPartitions', 151
  `NrPartitions', 151
  `NrPartitionsSet', 150
  `NrPartitionTuples', 153
  `NrPermutationsList', 149
  `NrPolyhedralSubgroups', 736
  `NrPrimitiveGroups', 520
  `NrRestrictedPartitions', 152
  `NrSubsTom', 699
  `NrTransitiveGroups', 511
  `NrTuples', 149
  `NrUnorderedTuples', 148
  `NullAlgebra', 609
  `NullMat', 222
  `NullspaceIntMat', 236
  `NullspaceMat', 225
  `NullspaceMatDestructive', 225
  `NullspaceModQ', 234
  `Number', 199
  number, Bell, 146
    \sub binomial, 145
    \sub Stirling, of the first kind, 146
    \sub Stirling, of the second kind, 147
  `NumberArgumentsFunction', 61
  `NumberFFVector', 213
  number field, 583
  number fields, Galois group, 586
  `NumberIrreducibleSolvableGroups', 522
  `NumberPerfectGroups', 516
  `NumberPerfectLibraryGroups', 516
  `NumberSmallGroups', 513
  `NumberSyllables', 331
  numerator, of a rational, 144
  `NumeratorOfModuloPcgs', 437
  `NumeratorOfRationalFunction', 662
  `NumeratorRat', 144
  Numerical Group Attributes, \indexit{363}
\letter O
  $O_p(G)$, see `PCore', 356
  `ObjByExtRep', 649
  Objects, \indexit{110}
  obsolete, 838
  `OCOneCocycles', 376
  octal character codes, 247
  `OctaveAlgebra', 609
  `od', 52
  `OldGeneratorsOfPresentation', 491
  `Omega', 360
  `ONanScottType', 412
  `OnBreak', 68
  `OnBreakMessage', 69
  `One', 288
  `OneAttr', 288
  `OneCoboundaries', 375
  `OneCocycles', 374
  one cohomology, 374
  `OneFactorBound', 669
  `OneImmutable', 288
  `OneIrreducibleSolvableGroup', 522
  `One<Library>Group', 511
  `OneMutable', 288
  `OneOfPcgs', 432
  `OneOp', 288
  `OnePrimitiveGroup', 511
  `OneSameMutability', 288
  `OneSM', 288
  `OneSmallGroup', 513
  `OneTransitiveGroup', 511
  `OnIndeterminates', 667
    \sub as a permutation action, 393
  `OnLeftInverse', 392
  `OnLines', 393
    \sub example, 506
  `OnPairs', 392
  `OnPoints', 392
  `OnRight', 392
  `OnSets', 392
  `OnSetsDisjointSets', 392
  `OnSetsSets', 392
  `OnSetsTuples', 392
  `OnSubspacesByCanonicalBasis', 394
  `OnTuples', 392
  `OnTuplesSets', 392
  `OnTuplesTuples', 393
  `Operation', 838
  `OperationAlgebraHomomorphism', 621
  Operational Structure of Domains, \indexit{282}
  `OperationHomomorphism', 838
  operations, for booleans, 168
  Operations and Attributes for Vector Spaces, \indexit{590}
  Operations applicable to All Streams, \indexit{98}
  Operations Concerning Blocks, \indexit{731}
  Operations for (Near-)Additive Magmas, \indexit{552}
  Operations for Abelian Number Fields, \indexit{583}
  operations for algebraic elements, 682
  Operations for Associative Words, \indexit{329}
  Operations for Associative Words by their Syllables, \indexit{331}
  Operations for Booleans, \indexit{168}
  Operations for Brauer Characters, \indexit{787}
  Operations for Class Functions, \indexit{765}
  Operations for Collections, \indexit{270}
  Operations for Cyclotomics, \indexit{155}
  Operations for Domains, \indexit{287}
  Operations for Finite Field Elements, \indexit{577}
  Operations for Finitely Presented Groups, \indexit{460}
  Operations for Group Homomorphisms, \indexit{381}
  Operations for Input Streams, \indexit{98}
  Operations for Lists, \indexit{194}
  Operations for Output Streams, \indexit{101}
  Operations for Pc Groups, \indexit{452}
  Operations for Rational Functions, \indexit{661}
  Operations for Special Kinds of Bases, \indexit{595}
  Operations for Stabilizer Chains, \indexit{418}
  Operations for Vector Space Bases, \indexit{593}
  Operations for Words, \indexit{323}
  Operations on elements of the algebra, \indexit{340}
  Operations on rewriting systems, \indexit{339}
  Operations to Evaluate Strings, \indexit{253}
  Operations to Produce or Manipulate Strings, \indexit{250}
  Operations which have Special Methods for Groups with Pcgs, \indexit{445}
  operators, 42
    \sub arithmetic, 48
    \sub associativity, 49
    \sub for cyclotomics, 159
    \sub for lists, 180
    \sub precedence, 48, 49
  Operators for Character Tables, \indexit{723}
  Operators for Matrices, \indexit{219}
  Operators for Row Vectors, \indexit{210}
  Optimization and Compiler Options, \indexit{827}
  options, 27, 819
    \sub command line, filenames, 29
    \sub command line, internal, 30
  options, under UNIX, 27
  `or', 168
  `Orbit', 394
  `OrbitFusions', 798
  `OrbitLength', 395
  `OrbitLengths', 395
  `OrbitLengthsDomain', 395
  `OrbitPerms', 410
  `OrbitPowerMaps', 793
  `Orbits', operation/attribute, 395
  Orbits, \indexit{394}
  `OrbitsDomain', 395
  `OrbitsPerms', 410
  `OrbitStabChain', 419
  `OrbitStabilizer', 396
  `OrbitStabilizerAlgorithm', 396
  Orbit Stabilizer Methods for Polycyclic Groups, \indexit{444}
  `Order', 291
    \sub of a class function, 762
  order,  of a group, 344
    \sub of a list, collection or domain, 269
    \sub of the prime residue group, 136
  `OrderedPartitions', 151
  ordering, booleans, 167
    \sub of records, 260
  `OrderingByLessThanFunctionNC', 276
  `OrderingByLessThanOrEqualFunctionNC', 276
  `OrderingOfRewritingSystem', 339
  `OrderingOnGenerators', 278
  `OrderingsFamily', 276
  Orderings on families of associative words, \indexit{277}
  `OrderMod', 137
  `OrderOfRewritingSystem', 339
  `OrdersClassRepresentatives', 727
  `OrdersTom', 699
  `Ordinal', 254
  ordinary character, 765
  `OrdinaryCharacterTable', 725
  `OrthogonalComponents', 778
  Orthogonal Embeddings, \indexit{242}
  `OrthogonalEmbeddings', 242
  `OrthogonalEmbeddingsSpecialDimension', 774
  OSX, 828
  Other Filters, \indexit{125}
  Other Operations Applicable to any Object, \indexit{115}
  Other Operations for Character Tables, \indexit{734}
  Other Operations for Tables of Marks, \indexit{702}
  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, 362
  package, 834
  Package Interface - Obsolete Functions and Name Changes, \indexit{838}
  Packages, \indexit{823}
  `PadicCoefficients', 241
  `PadicExtensionNumberFamily', 685
  `PadicNumber', 685
    \sub for pure padics, 684
  `Pager', 25
  `Parametrized', 801
  Parametrized Maps, \indexit{799}
  parametrized maps, 790
  `Parent', 286
  `ParentPcgs', 435
  Parents, \indexit{286}
  partial order, 311
  `PartialOrderByOrderingFunction', 312
  `PartialOrderOfHasseDiagram', 311
  `Partitions', 151
  partitions, improper, of an integer, 151
    \sub ordered, of an integer, 151
    \sub restricted, of an integer, 152
  `PartitionsGreatestEQ', 152
  `PartitionsGreatestLE', 152
  `PartitionsSet', 150
  `PartitionTuples', 153
  `PcElementByExponents', 433
  `PcElementByExponentsNC', 433
  `PCentralLieAlgebra', 641
  `PCentralNormalSeriesByPcgsPGroup', 440
  `PCentralSeries', 366
  `PcGroupCode', 456
  `PcGroupCodeRec', 456
  `PcGroupFpGroup', 449
  Pc groups versus fp groups, \indexit{448}
  `PcGroupWithPcgs', 451
  `Pcgs', 431
  `Pcgs_OrbitStabilizer', 445
  Pcgs and Normal Series, \indexit{438}
  `PcgsByPcSequence', 431
  `PcgsByPcSequenceNC', 431
  `PcgsCentralSeries', 439
  `PcgsChiefSeries', 440
  `PcgsElementaryAbelianSeries', 439
  `PcgsPCentralSeriesPGroup', 440
  `PClassPGroup', 362
  `PCore', 356
  `PcSeries', 432
  `PerfectGroup', 515
  perfect groups, 515
  `PerfectIdentification', 516
  `PerfectResiduum', 358
  `Perform', 196
  `Permanent', 154
  Permanent of a Matrix, \indexit{154}
  `PermBounds', 787
  `PermCharInfo', 782
  `PermCharInfoRelative', 783
  `PermChars', 783
  `PermCharsTom', 712
  `PermComb', 787
  `PermLeftQuoTransformation', 549
  `PermList', 408
  `PermListList', 196
  `Permutation', 400
  `PermutationCharacter', 764
  permutation character, 809
  permutation characters, possible, 781, 783
  `PermutationCycle', 400
  `PermutationMat', 223
  `PermutationsFamily', 406
  Permutations Induced by Elements and Cycles, \indexit{400}
  `PermutationsList', 149
  `PermutationTom', 697
  `Permuted', 198
    \sub as a permutation action, 393
    \sub for class functions, 762
  `PGL', 507
  `PGU', 508
  `Phi', 136
  point stabilizer, 396
  Polycyclic Generating Systems, \indexit{430}
  `PolynomialByExtRep', 679
  `PolynomialCoefficientsOfPolynomial', 665
  `PolynomialDivisionAlgorithm', 675
  Polynomial Factorization, \indexit{667}
  `PolynomialModP', 668
  `PolynomialReducedRemainder', 675
  `PolynomialReduction', 675
  `PolynomialRing', 670
  Polynomial Rings, \indexit{670}
  Polynomials as Univariate Polynomials in one Indeterminate, \indexit{665}
  polynomials over abelian number fields, factors, 583
  Polynomials over the Rationals, \indexit{668}
  `PopOptions', 88
  Portability, \indexit{90}
  Porting GAP, \indexit{827}
  `Position', 187
  `PositionBound', 189
  `PositionCanonical', 187
  `PositionNonZero', 189
  `PositionNot', 189
  `PositionNthOccurrence', 188
  `PositionProperty', 189
  `PositionSet', 188
  `PositionSorted', 188
  `PositionStream', 100
  `PositionSublist', 190
  `PositionWord', 330
  `PositiveIntegers', 126
  positive number, 48
  `PositiveRoots', 637
  `PositiveRootVectors', 637
  `PossibleClassFusions', 797
  `PossibleFusionsCharTableTom', 711
  Possible Permutation Characters, \indexit{781}
  possible permutation characters, 781, 783
  `PossiblePowerMaps', 791
  power, 48
    \sub matrix, 220
    \sub meaning for class functions, 761
    \sub of words, 329
  `PowerMap', 791
  `PowerMapByComposition', 793
  `PowerMapOp', 791
  Power Maps, \indexit{790}
  `PowerMapsAllowedBySymmetrizations', 808
  `PowerMod', 564
  `PowerModCoeffs', 216
  `PowerModInt', 131
  `PowerPartition', 153
  powerset, 147
  `PowerSubalgebraSeries', 614
  `PQuotient', 471
  precedence, 48
  precedence test, for permutations, 407
  `PrefrattiniSubgroup', 358
    \sub for groups with pcgs, 445
  `PreImage', 304
  `PreImageElm', 303
  `PreImages', 304
  `PreImagesElm', 303
  Preimages in the Free Group, \indexit{459}
  Preimages in the Free Semigroup, \indexit{543}
  `PreimagesOfTransformation', 548
  `PreImagesRange', 303
  `PreImagesRepresentative', 304
  `PreImagesSet', 304
  Preimages under Homomorphisms from an FpGroup, \indexit{470}
  Preimages under Mappings, \indexit{303}
  preorder, 311
  `PresentationFpGroup', 475
  `PresentationNormalClosure', 480
  `PresentationNormalClosureRrs', 480
  `PresentationSubgroup', 477
  `PresentationSubgroupMtc', 479
  `PresentationSubgroupRrs', 478
  `PresentationViaCosetTable', 476
  previous result, 64
  `PrevPrimeInt', 132
  `PrimaryGeneratorWords', 479
  primary subgroup generators, 493
  `PrimeBlocks', 731
  `PrimeBlocksOp', 731
  `PrimeField', 572
  Prime Integers and Factorization, \indexit{131}
  `PrimePGroup', 362
  `PrimePowersInt', 133
  prime residue group, 136
    \sub exponent, 136
    \sub generator, 138
    \sub order, 136
  Prime Residues, \indexit{136}
  `PrimeResidues', function, 136
  `Primes', 131
  primitive, 401
  `PRIMITIVE_INDICES_MAGMA', 521
  `PrimitiveElement', 572
  `PrimitiveGroup', 520
  Primitive Groups, \indexit{412}
  `PrimitiveGroupsIterator', 520
  `PrimitiveIdentification', 521
  `PrimitiveIndexIrreducibleSolvableGroup', 522
  Primitive Permutation Groups, \indexit{519}
  `PrimitivePolynomial', 668
  `PrimitiveRoot', 579
  `PrimitiveRootMod', 138
  primitive root modulo an integer, 138
  Primitive Roots and Discrete Logarithms, \indexit{137}
  Primitivity of Characters, \indexit{813}
  `Print', 65
  `PrintAmbiguity', 804
  `PrintArray', 224
  `PrintCharacterTable', 739
  `PrintFactorsInt', 133
  `PrintFormattingStatus', 102
  Printing Character Tables, \indexit{737}
  Printing Class Functions, \indexit{762}
  Printing Presentations, \indexit{481}
  Printing Tables of Marks, \indexit{696}
  `PrintObj', 66
    \sub for character tables, 737, 762
    \sub for tables of marks, 696
  `PrintTo', 95
    \sub for streams, 101
  `ProbabilityShapes', 668
  problems, 824
  Problems on Particular Systems, \indexit{827}
  procedure call, 50
  Procedure Calls, \indexit{50}
  procedure call with arguments, 50
  `Process', 108
  Process, \indexit{108}
  `PROD_GF2MAT_GF2MAT_ADVANCED', 234
  `PROD_GF2MAT_GF2MAT_SIMPLE', 234
  `Product', 200
  product, of words, 329
    \sub rational functions, 661
  `ProductCoeffs', 216
  `ProductSpace', 614
  `ProductX', 203
  `ProfileFunctions', 82
  `ProfileGlobalFunctions', 82
  `ProfileMethods', 82
  `ProfileOperations', 81
  `ProfileOperationsAndMethods', 81
  `PROFILETHRESHOLD', 82
  Profiling, \indexit{81}
  `ProjectedInducedPcgs', 438
  `ProjectedPcElement', 438
  `Projection', 301
    \sub example for direct products, 498
    \sub example for semidirect products, 500
    \sub example for subdirect products, 500
    \sub example for wreath products, 501
    \sub for group products, 502
  `ProjectionMap', 800
  projections, find all, 388
  `ProjectiveActionHomomorphismMatrixGroup', 425
  `ProjectiveActionOnFullSpace', 425
  `ProjectiveGeneralLinearGroup', 507
  `ProjectiveGeneralUnitaryGroup', 508
  `ProjectiveOrder', 233
  `ProjectiveSpecialLinearGroup', 508
  `ProjectiveSpecialUnitaryGroup', 508
  `ProjectiveSymplecticGroup', 508
  prompt, 64
    \sub partial, 64
  Properties, \indexit{124}
  Properties and Attributes for Lists, \indexit{190}
  Properties and Attributes of (General) Mappings, \indexit{301}
  Properties and Attributes of Binary Relations, \indexit{310}
  Properties and Attributes of Matrices, \indexit{221}
  Properties and Attributes of Rational Functions, \indexit{662}
  Properties and basic functionality, \indexit{276}
  Properties of a Lie Algebra, \indexit{635}
  Properties of rewriting systems, \indexit{340}
  Properties of Rings, \indexit{559}
  Properties of Tables of Marks, \indexit{702}
  `PRump', 359
  `PseudoRandom', 272
  `PSL', 508
  `PSP', 508
  `PSp', 508
  `PSU', 508
  `PthPowerImage', 641
  `PthPowerImages', 640
  Pure p-adic Numbers, \indexit{684}
  `PurePadicNumberFamily', 684
  `PushOptions', 88
\letter Q
  `Quadratic', 162
  quadratic residue, 138, 139
  `QuaternionAlgebra', 609
  `QUIET', 839
  `QUIT', emergency quit, 72
  quit, in emergency, 72
  `quit', 67
  `QUITTING', 72
  `QuoInt', 129
  `Quotient', 555
  quotient, for finitely presented groups, 458
    \sub matrices, 220
    \sub matrix and matrix list, 221
    \sub matrix and scalar, 220
    \sub of free monoid, 544
    \sub of free semigroup, 542
    \sub of words, 329
    \sub rational functions, 661
    \sub scalar and matrix, 220
    \sub scalar and matrix list, 220
    \sub vector and matrix, 220
  `QuotientFromSCTable', 608
  Quotient Methods, \indexit{471}
  `QuotientMod', 564
  `QuotientPolynomialsExtRep', 680
  `QuotientRemainder', 563
  Quotients, \indexit{534}
  Quotients and Remainders, \indexit{129}
  `QuotientSemigroupCongruence', 534
  `QuotientSemigroupHomomorphism', 534
  `QuotientSemigroupPreimage', 534
  `QuotRemLaurpols', 670
\letter R
  $r_N$, 160
  `RadicalGroup', 358
  `RadicalOfAlgebra', 617
  `Random', 272
    \sub for integers, 128
    \sub for rationals, 144
  `RandomBinaryRelationOnPoints', 312
  random element, of a list or collection, 272
  Random Elements, \indexit{272}
  `RandomInvertibleMat', 224
  `RandomIsomorphismTest', 456
  Random Isomorphism Testing, \indexit{456}
  Randomized Methods for Permutation Groups, \indexit{414}
  `RandomList', 273
  `RandomMat', 224
  Random Matrices, \indexit{224}
  `RandomPrimitivePolynomial', 581
  random seed, 273
  `RandomTransformation', 547
  `RandomUnimodularMat', 224
  `Range', 302
  range, 203
  Ranges, \indexit{203}
  `RankAction', 401
  `RankFilter', 117
  `RankMat', 225
  `RankOfTransformation', 548
  `RankPGroup', 363
  `Rat', 144
    \sub for strings, 253
  `RationalClass', 355
  `RationalClasses', 355
  `RationalFunctionByExtRep', 679
  `Rational\-Function\-By\-Ext\-Rep\-With\-Cancellation', 680
  Rational Function Families, \indexit{677}
  `RationalFunctionsFamily', 677
  `RationalizedMat', 163
  `Rationals', 143
  `RClassOfHClass', 535
  `Read', 94
    \sub for streams, 98
  `ReadAll', 100
  `ReadAllLine', 105
  `ReadAsFunction', 94
    \sub for streams, 99
  `ReadByte', 99
  read eval print loop, 64
  `ReadLine', 99
  `ReadPackage', 835
  `ReadPkg', 838
  `ReadTest', 84
    \sub for streams, 99
  `RealClasses', 729
  `RealizableBrauerCharacters', 788
  `RecNames', 257
  Recognizing Characters, \indexit{249}
  record, component access, 257
    \sub component assignment, 258
    \sub component variable, 258
    \sub component variable assignment, 259
  Record Access Operations, \indexit{262}
  Record Assignment, \indexit{258}
  record assignment, operation, 262
  record boundness test, operation, 262
  record component, operation, 262
  record unbind, operation, 262
  Recovery from NoMethodFound-Errors, \indexit{76}
  recursion, 55
  redisplay a help section, 23
  redisplay with next help viewer, 23
  `ReduceCoeffs', 216
  `ReduceCoeffsMod', 216
  `ReducedAdditiveInverse', 340
  `ReducedCharacters', 771
  `ReducedClassFunctions', 771
  `ReducedComm', 340
  `ReducedConfluentRewritingSystem', 544
  `ReducedConjugate', 340
  `ReducedDifference', 340
  `ReducedForm', 339
  `ReducedGroebnerBasis', 676
  `ReducedInverse', 340
  `ReducedLeftQuotient', 340
  `ReducedOne', 340
  `ReducedPcElement', 433
  `ReducedPower', 340
  `ReducedProduct', 340
  `ReducedQuotient', 340
  `ReducedScalarProduct', 340
  `ReducedSum', 340
  `ReducedZero', 340
  `ReduceRules', 340
  `ReduceStabChain', 420
  Reducing Virtual Characters, \indexit{771}
  `Ree', 505
  `ReeGroup', 505
  `ReesCongruenceOfSemigroupIdeal', 533
  `ReesMatrixSemigroup', 536
  `ReesMatrixSemigroupElement', 536
  Rees Matrix Semigroups, \indexit{536}
  `ReesZeroMatrixSemigroup', 536
  `ReesZeroMatrixSemigroupElement', 536
  `ReesZeroMatrixSemigroupElementIsZero', 537
  `RefinedPcGroup', 451
  `ReflectionMat', 224
  `ReflexiveClosureBinaryRelation', 312
  reflexive relation, 310
  regular, 401
  regular action, 398
  `RegularActionHomomorphism', 399
  `RegularModule', 742
  relations, 299
  Relations Between Domains, \indexit{292}
  `RelationsOfFpSemigroup', 543
  `RelativeBasis', 593
  `RelativeBasisNC', 593
  relatively prime, 48
  `RelativeOrderOfPcElement', 432
  `RelativeOrders', of a pcgs, 432
  Relators in a Presentation, \indexit{480}
  `RelatorsOfFpGroup', 459
  remainder, operation, 292
  remainder of a quotient, 129
  `RemInt', 129
  remove, an element from a set, 194
  `RemoveFile', 95
  `RemoveOuterCoeffs', 214
  `RemoveRelator', 483
  `RemoveSet', 194
  `RemoveStabChain', 420
  Repeat, \indexit{52}
  `repeat' loop, 52
  `ReplacedString', 251
  Representation, \indexit{120}
  representation, as a sum of two squares, 142
  Representations for Associative Words, \indexit{332}
  Representations for Group Homomorphisms, \indexit{389}
  Representations given by modules, \indexit{742}
  Representations of Algebras, \indexit{622}
  `RepresentationsOfObject', 121
  `Representative', 269
  representative, of a list or collection, 269
  `RepresentativeAction', 396
  `RepresentativeLinearOperation', 622
  `RepresentativeOperation', 838
  `RepresentativesContainedRightCosets', 353
  `RepresentativesFusions', 798
  `RepresentativeSmallest', 269
  `RepresentativesMinimalBlocks', 402
  `RepresentativesPerfectSubgroups', 371
  `RepresentativesPowerMaps', 793
  `RepresentativesSimpleSubgroups', 371
  `RepresentativeTom', 710
  `RepresentativeTomByGenerators', 710
  `RepresentativeTomByGeneratorsNC', 710
  `RequirePackage', 838
  `Reread', 96
  `REREADING', 96
  `RereadPackage', 835
  `RereadPkg', 838
  `ResetOptionsStack', 88
  residue, quadratic, 138, 139
  Residue Class Rings, \indexit{133}
  `RespectsAddition', 306
  `RespectsAdditiveInverses', 306
  `RespectsInverses', 306
  `RespectsMultiplication', 305
  `RespectsOne', 306
  `RespectsScalarMultiplication', 307
  `RespectsZero', 307
  `RestoreStateRandom', 272
  Restricted and Induced Class Functions, \indexit{769}
  `RestrictedClassFunction', 769
  `RestrictedClassFunctions', 770
  Restricted Lie algebras, \indexit{640}
  `RestrictedMapping', 301
  `RestrictedPartitions', 152
  `RestrictedPerm', 409
  `RestrictedTransformation', 548
  `Resultant', 666
  `ResultOfStraightLineProgram', 335
  Return, \indexit{58}
  `return', 67
    \sub no value, 58
    \sub with value, 58
  `ReturnFail', 63
  `ReturnFalse', 62
  return from break loop, 67
  `ReturnTrue', 62
  `Reversed', 196
  `RewindStream', 100
  `RewriteWord', 465
  Rewriting in Groups and Monoids, \indexit{341}
  Rewriting Systems and the Knuth-Bendix Procedure, \indexit{544}
  `RightActingAlgebra', 625
  `RightActingRingOfIdeal', 558
  `RightAlgebraModule', 623
  `RightAlgebraModuleByGenerators', 623
  `RightCoset', 351
  `RightCosets', 351
  right cosets, 351
  `RightCosetsNC', 351
  `RightDerivations', 632
  `RightIdeal', 556
  `RightIdealByGenerators', 557
  `RightIdealNC', 557
  `RightModuleByHomomorphismToMatAlg', 626
  `RightShiftRowVector', 214
  `RightTransversal', 352
  `Ring', 554
  `RingByGenerators', 555
  Ring Homomorphisms, \indexit{308}
  Rings With One, \indexit{558}
  `RingWithOne', 558
  `RingWithOneByGenerators', 558
  `RNamObj', 262
  root, of 1 modulo an integer, 140
    \sub of an integer, 128
    \sub of an integer, smallest, 128
    \sub of an integer modulo another, 139
  `RootInt', 128
  `RootMod', 139
  `RootOfDefiningPolynomial', 572
  `RootsMod', 139
  Roots Modulo Integers, \indexit{138}
  roots of unity, 155
  `RootsOfUPol', 665
  `RootsUnityMod', 140
  `RootSystem', 637
  `RoundCyc', 157
  Row and Matrix Spaces, \indexit{597}
  `RowIndexOfReesMatrixSemigroupElement', 537
  `Row\-Index\-Of\-Rees\-Zero\-Matrix\-Semigroup\-Element', 537
  row spaces, 597
  Row Vectors over Finite Fields, \indexit{212}
  `Rules', 339
  Running GAP under MacOS, \indexit{30}
  `Runtime', 81
  `Runtimes', 80
\letter S
  $s_N$, 160
  `SameBlock', 732
  `SandwichMatrixOfReesMatrixSemigroup', 537
  `SandwichMatrixOfReesZeroMatrixSemigroup', 537
  save, 36
  `SaveOnExitFile', 73
  `SaveWorkspace', 36
  Saving and Loading a Workspace, \indexit{36}
  Saving a Pc Group, \indexit{452}
  saving on exit, 72
  `ScalarProduct', for characters, 766
  Schreier, 477
  Schreier-Sims, random, 414
  `SchurCover', 377
  Schur Covers and Multipliers, \indexit{376}
  Schur multiplier, 377
  scope, 42
  `ScriptFromString', 707
  Searching for Homomorphisms, \indexit{387}
  `SecHMSM', 255
  secondary subgroup generators, 493
  `SecondsDMYhms', 255
  `SeekPositionStream', 101
  Selecting a Different MeatAxe, \indexit{687}
  Selection Functions, \indexit{510}
  `SemidirectProduct', 499
  Semidirect Products, \indexit{498}
  `SemiEchelonBasis', 599
  `SemiEchelonBasisNC', 599
  `SemiEchelonMat', 227
  `SemiEchelonMatDestructive', 227
  `SemiEchelonMats', 228
  `SemiEchelonMatsDestructive', 228
  `SemiEchelonMatTransformation', 228
  `Semigroup', 531
  semigroup, 531
  `SemigroupByGenerators', 531
  `SemigroupByMultiplicationTable', 532
  `SemigroupIdealByGenerators', 533
  `SemigroupOfRewritingSystem', 546
  semiregular, 401
  Semisimple Lie Algebras and Root Systems, \indexit{636}
  `SemiSimpleType', 636
  sequence, Bernoulli, 146
    \sub Fibonacci, 153
    \sub Lucas, 154
  Series of Ideals, \indexit{634}
  `Set', 266
  `SetAssertionLevel', 80
  `SetCommutator', 450
  `SetConjugate', 450
  `SetCrystGroupDefaultAction', 429
  set difference, of collections, 271
  `SetEntrySCTable', 607
  `SetGasmanMessageStatus', 86
  `SetHelpViewer', 24
  `SetIndeterminateName', 660
  `SetInfoLevel', 79
  `SetName', 115
  Set Operations via Boolean Lists, \indexit{207}
  `SetParent', 286
  `SetPower', 450
  `SetPrintFormattingStatus', 102
  `SetRecursionTrapInterval', 85
  `SetReducedMultiplication', 459
  Sets, \indexit{110}
  sets, 170, 192
  Sets of Subgroups, \indexit{367}
  set stabilizer, 396
  `Setter', 122
  setter, 121
  Setter and Tester for Attributes, \indexit{121}
  `SetX', 202
  `ShallowCopy', 114
    \sub for lists, 177
  `ShiftedCoeffs', 216
  `ShiftedPadicNumber', 684
  Shifting and Trimming Coefficient Lists, \indexit{214}
  `ShortestVectors', 243
  `ShortLexOrdering', 279
  short vectors spanning a lattice, 241, 772
  `ShowArgument', 76
  `ShowArguments', 76
  `ShowDetails', 76
  `ShowImpliedFilters', 118
  `ShowMethods', 76
  `ShowOtherMethods', 77
  `ShrinkCoeffs', 216
  `ShrinkRowVector', 214
  `SiftedPcElement', 433
  `SiftedPermutation', 419
  `SiftedVector', 600
  `Sigma', 140
  sign, of an integer, 127
  Sign and Cycle Structure, \indexit{408}
  `SignInt', 127
  `SignPartition', 152
  `SignPerm', 408
  `SimpleLieAlgebra', 632
  `SimpleSystem', 637
  `SimplifiedFpGroup', 477
  SimplifiedFpGroup, \indexit{477}
  `SimplifyPresentation', 484
  `SimsNo', 521
  `SimultaneousEigenvalues', 233
  `SingleCollector', 450
  singlequote character, 247
  singlequotes, 245
  `SINT_CHAR', 253
  `Size', 269
    \sub for character tables, 726
    \sub for groups with pcgs, 445
  size, of a list or collection, 269
  `SizeBlist', 207
  `SizeConsiderFunction', 373
  `SizeNumbersPerfectGroups', 516
  `SizeOfFieldOfDefinition', 788
  `SizesCentralizers', 727
  `SizesConjugacyClasses', 727
  `SizeScreen', 75
  SizeScreen, \indexit{75}
  `SizesPerfectGroups', 515
  `SizeStabChain', 418
  `SL', 506
  smaller, associative words, 329
    \sub elements of finitely presented groups, 459
    \sub nonassociative words, 322
    \sub pcwords, 448
    \sub rational functions, 661
  `SmallerDegreePermutationRepresentation', 411
  smaller or equal, 47
  smaller test, 47
  `SmallestGeneratorPerm', 407
  `SmallestMovedPoint', 407
  `SmallestRootInt', 128
  `SmallGeneratingSet', 374
  `SmallGroup', 513
  Small Groups, \indexit{512}
  `SmallGroupsInformation', 513
  Smash MeatAxe Flags, \indexit{691}
  smith normal form, 838
  `SmithNormalFormIntegerMat', 238
  `SmithNormalFormIntegerMatTransforms', 238
  `SMTX.AbsoluteIrreducibilityTest', 691
  `SMTX.AlgEl', 691
  `SMTX.AlgElCharPol', 692
  `SMTX.AlgElCharPolFac', 692
  `SMTX.AlgElMat', 691
  `SMTX.AlgElNullspaceDimension', 692
  `SMTX.AlgElNullspaceVec', 692
  `SMTX.CentMat', 692
  `SMTX.CentMatMinPoly', 692
  `SMTX.CompleteBasis', 691
  `SMTX.Getter', 691
  `SMTX.GoodElementGModule', 691
  `SMTX.IrreducibilityTest', 691
  `SMTX.MatrixSum', 691
  `SMTX.MinimalSubGModule', 691
  `SMTX.MinimalSubGModules', 691
  `SMTX.RandomIrreducibleSubGModule', 691
  `SMTX.Setter', 691
  `SMTX.SortHomGModule', 691
  `SMTX.Subbasis', 691
  `SO', 507
  `Socle', 358
  `SocleTypePrimitiveGroup', 412
  `SolutionIntMat', 236
  `SolutionMat', 226
  `SolutionMatDestructive', 226
  `SolutionNullspaceIntMat', 236
  Some Remarks about Character Theory in GAP, \indexit{715}
  Some Special Algebras, \indexit{609}
  `Sort', 191
  `SortedCharacters', 749
  `SortedCharacterTable', 750
  Sorted Character Tables, \indexit{749}
  `SortedList', 266
  sorted list, 190
  Sorted Lists and Sets, \indexit{192}
  sorted lists as collections, 264
  `SortedSparseActionHomomorphism', 398
  `SortedTom', 697
  `Sortex', 192
  Sorting Lists, \indexit{191}
  `SortingPerm', 192
  Sorting Tables of Marks, \indexit{697}
  `SortParallel', 191
  `Source', 302
  `SP', 507
  `Sp', 507
  space, 40
  `SparseActionHomomorphism', 398
  `SparseCartanMatrix', 638
  Special Characters, \indexit{247}
  special character sequences, 247
  Special Filenames, \indexit{92}
  Special Generating Sets, \indexit{374}
  `SpecialLinearGroup', 506
  Special Multiplication Algorithms for Matrices over GF(2), \indexit{234}
  `SpecialOrthogonalGroup', 507
  Special Pcgs, \indexit{441}
  `SpecialPcgs', attribute, 442
  `SpecialUnitaryGroup', 506
  Specific and Parametrized Subgroups, \indexit{357}
  Specific Methods for Subgroup Lattice Computations, \indexit{371}
  `SplitCharacters', 744
  `SplitExtension', 453
  `SplitExtensions', 455
  `SplitString', 250
  `SplittingField', 664
  `Sqrt', 292
  square root, of an integer, 128
  `SquareRoots', 319
  `SSortedList', 266
  `StabChain', 415
  `StabChainBaseStrongGenerators', 417
  `StabChainImmutable', 415
  `StabChainMutable', 415
  `StabChainOp', 415
  `StabChainOptions', 417
  `Stabilizer', 396
  Stabilizer Chain Records, \indexit{417}
  Stabilizer Chains, \indexit{413}
  `StabilizerOfExternalSet', 404
  `StabilizerPcgs', 445
  Stabilizers, \indexit{396}
  `StandardAssociate', 561
  `StandardGeneratorsFunctions', 707
  `StandardGeneratorsInfo', for groups, 706
    \sub for tables of marks, 710
  `StandardGeneratorsOfGroup', 708
  Standard Generators of Groups, \indexit{706}
  Standardization of coset tables, \indexit{464}
  `StandardizeTable', 464
  `StarCyc', 162
  Statements, \indexit{49}
  `StateRandom', 272
  `Stirling1', 146
  `Stirling2', 146
  Stirling number of the first kind, 146
  Stirling number of the second kind, 147
  `StoredGroebnerBasis', 676
  `StoreFusion', 796
  Storing Normal Subgroup Information, \indexit{753}
  `StraightLineProgElm', 338
  `StraightLineProgGens', 338
  `StraightLineProgram', 334
  Straight Line Program Elements, \indexit{337}
  `StraightLineProgramNC', 334
  Straight Line Programs, \indexit{334}
  `StraightLineProgramsTom', 709
  `StreamsFamily', 98
  `StretchImportantSLPElement', 338
  strictly sorted list, 191
  `String', 250
    \sub for cyclotomics, 156
  `StringDate', 255
  `StringOfResultOfStraightLineProgram', 336
  `StringPP', 250
  strings, equality of, 249
    \sub inequality of, 249
    \sub lexicographic ordering of, 249
  String Streams, \indexit{104}
  `StringTime', 255
  `StrongGeneratorsStabChain', 418
  `StronglyConnectedComponents', 312
  <Struct>, 283
  `<Struct>ByGenerators', 284
  `StructuralCopy', 114
    \sub for lists, 178
  structure constant, 736, 737
  `StructureConstantsTable', 595
  `StructureDescription', 349
  Structure Descriptions, \indexit{349}
  `<Struct>WithGenerators', 284
  `SU', 506
  `Subalgebra', 610
  `SubAlgebraModule', 626
  `SubalgebraNC', 610
  Subalgebras, \indexit{610}
  `SubalgebraWithOne', 610
  `SubalgebraWithOneNC', 611
  `SubdirectProduct', 500
  Subdirect Products, \indexit{500}
  `SubdirectProducts', 501
  subdomains, 287
  `Subfield', 571
  `SubfieldNC', 571
  `Subfields', 572
  Subfields of Fields, \indexit{571}
  `Subgroup', 346
  `SubgroupByPcgs', 436
  `SubgroupByProperty', 347
  subgroup fusions, 794
  subgroup generators tree, 493
  Subgroup Lattice, \indexit{369}
  `SubgroupNC', 346
  `SubgroupOfWholeGroupByCosetTable', 465
  `SubgroupOfWholeGroupByQuotientSubgroup', 470
  Subgroup Presentations, \indexit{477}
  `SubgroupProperty', 421
  Subgroups, \indexit{345}
  subgroups, polyhedral, 736
  Subgroups characterized by prime powers, \indexit{360}
  Subgroup Series, \indexit{363}
  `SubgroupShell', 347
  Subgroups of Polycyclic Groups - Canonical Pcgs, \indexit{436}
  Subgroups of Polycyclic Groups - Induced Pcgs, \indexit{434}
  `SubgroupsSolvableGroup', 372
  sublist, 172
    \sub access, 172
    \sub assignment, 174
    \sub operation, 173
  sublist assignment, operation, 175
  `Submagma', 316
  `SubmagmaNC', 316
  `SubmagmaWithInverses', 316
  `SubmagmaWithInversesNC', 316
  `SubmagmaWithOne', 316
  `SubmagmaWithOneNC', 316
  `Submodule', 567
  `SubmoduleNC', 567
  Submodules, \indexit{567}
  `Submonoid', 538
  `SubmonoidNC', 538
  `SubnearAdditiveGroup', 552
  `SubnearAdditiveGroupNC', 552
  `SubnearAdditiveMagma', 551
  `SubnearAdditiveMagmaNC', 551
  `SubnearAdditiveMagmaWithZero', 551
  `SubnearAdditiveMagmaWithZeroNC', 551
  `SubnormalSeries', 364
  `Subring', 555
  `SubringNC', 555
  `SubringWithOne', 559
  `SubringWithOneNC', 559
  Subroutines for the Construction of Class Fusions, \indexit{809}
  Subroutines for the Construction of Power Maps, \indexit{807}
  `Subsemigroup', 531
  `SubsemigroupNC', 531
  subsets, 147
  subset test, for collections, 270
  `Subspace', 589
  `SubspaceNC', 589
  `Subspaces', 590
  `SubstitutedWord', 331
  `SubsTom', 698
  `Sub<struct>', 287
  `Sub<struct>NC', 287
  `SubSyllables', 332
  subtract, a set from another, 194
  `SubtractBlist', 208
  subtraction, 48
    \sub matrices, 219
    \sub matrix and scalar, 219
    \sub rational functions, 661
    \sub scalar and matrix, 219
    \sub scalar and matrix list, 220
    \sub scalar and vector, 211
    \sub vector and scalar, 211
    \sub vectors, 211
  `SubtractSet', 194
  `Subword', 330
  `Successors', 311
  Suitability for Compilation, \indexit{35}
  `Sum', 201
  Sum and Intersection of Pcgs, \indexit{441}
  `SumFactorizationFunctionPcgs', 441
  `SumIntersectionMat', 229
  `SumX', 202
  `SupersolvableResiduum', 359
  `support', email address, 826
  `SupportedCharacterTableInfo', 719
  `SurjectiveActionHomomorphismAttr', 405
  `SuzukiGroup', 505
  `SylowComplement', 359
  `SylowSubgroup', 359
  Sylow Subgroups and Hall Subgroups, \indexit{359}
  `SylowSystem', 360
  Symbols, \indexit{40}
  Symmetric and Alternating Groups, \indexit{411}
  `SymmetricClosureBinaryRelation', 312
  `SymmetricGroup', 505
  symmetric group, powermap, 153
  `SymmetricParentGroup', 412
  `SymmetricParts', 778
  `SymmetricPowerOfAlgebraModule', 651
  symmetric relation, 310
  `Symmetrizations', 777
  symmetrizations, orthogonal, 778
    \sub symplectic, 779
  Symmetrizations of Class Functions, \indexit{777}
  `SymplecticComponents', 779
  `SymplecticGroup', 507
  syntax errors, 64
  system getter, 121
  system setter, 121
  `Sz', 505
\letter T
  $t_N$, 160
  `TableAutomorphisms', 752
  table automorphisms, 798, 810
  table of chapters for help books, 23
  `TableOfMarks', 694
  `TableOfMarksByLattice', 695
  `TableOfMarksComponents', 698
  `TableOfMarksCyclic', 712
  `TableOfMarksDihedral', 713
  `TableOfMarksFamily', 698
  `TableOfMarksFrobenius', 713
  Table of Marks Objects in GAP, \indexit{693}
  table of sections for help books, 23
  tables, 715, 717
  tabulator, 40
  `Tau', 140
  Technical Details about Tables of Marks, \indexit{698}
  Technical Details about the Implementation of Magma Rings, \indexit{657}
  Technical Matters Concerning General Mappings, \indexit{308}
  `TemporaryGlobalVarName', 45
  `Tensored', 769
  `TensorProductGModule ', 687
  `TensorProductOfAlgebraModules', 650
  Tensor Products and Exterior and Symmetric Powers, \indexit{650}
  test, for a primitive root, 138
    \sub for a rational, 143
    \sub for records, 257
    \sub for set equality, 193
  `TestConsistencyMaps', 803
  `Tester', 122
  tester, 121
  Test Files, \indexit{84}
  `TestHomogeneous', 813
  `TestInducedFromNormalSubgroup', 815
  Testing Finiteness of Finitely Presented Groups, \indexit{474}
  Testing for the System Architecture, \indexit{34}
  Testing Monomiality, \indexit{815}
  `TestJacobi', 607
  `TestMonomial', 815
  `TestMonomialQuick', 816
  `TestMonomialUseLattice', 816
  Test of the installation, \indexit{822}
  `TestPackageAvailability', 835
  `TestPerm1', 785
  `TestPerm2', 785
  `TestPerm3', 785
  `TestPerm4', 785
  `TestPerm5', 785
  `TestQuasiPrimitive', 814
  `TestRelativelySM', 817
  Tests for Actions, \indexit{400}
  Tests for the Availability of Methods, \indexit{377}
  `TestSubnormallyMonomial', 817
  The .gaprc file, \indexit{33}
  The Adjoint Representation, \indexit{641}
  The Compiler, \indexit{34}
  The Defining Attributes of Rational Functions, \indexit{678}
  The Dixon-Schneider Algorithm, \indexit{742}
  The Documentation, \indexit{823}
  The External Representation for Associative Words, \indexit{333}
  The family pcgs, \indexit{447}
  The Interface between Character Tables and Groups, \indexit{721}
  The Interface between Tables of Marks and Character Tables, \indexit{711}
  The Library of Tables of Marks, \indexit{713}
  `then', 51
  The Natural Action, \indexit{410}
  The Pager Command, \indexit{25}
  The Permutation Image of an Action, \indexit{397}
  The Representations of Rational Functions, \indexit{677}
  The Smash MeatAxe, \indexit{690}
  The Syntax in BNF, \indexit{58}
  `ThreeGroup' library, 512
  Tietze Options, \indexit{496}
  Tietze Transformations, \indexit{483}
  Tietze Transformations that introduce new Generators, \indexit{487}
  `TietzeWordAbstractWord', 481
  `time', 81
  Timing, \indexit{80}
  Todd-Coxeter Procedure, \indexit{546}
  `Trace', 221
    \sub for field elements, 573
    \sub of a matrix, 221
  `TracedCosetFpGroup', 461
  `TraceImmediateMethods', 78
  `TraceMat', 221
  `TraceMethods', 78
  `TracePolynomial', 573
  Tracing generator images through Tietze transformations, \indexit{491}
  Tracing Methods, \indexit{78}
  `TransferDiagram', 803
  `Transformation', 547
  `TransformationData', 547
  `TransformationFamily', 547
  `TransformationNC', 547
  `TransformationRelation', 549
  `TransformationType', 547
  `TransformingPermutations', 752
  `TransformingPermutationsCharacterTables', 752
  transitive, 400
  `TransitiveClosureBinaryRelation', 312
  `TransitiveGroup', 511
  `TransitiveIdentification', 511
  Transitive Permutation Groups, \indexit{511}
  transitive relation, 310
  `Transitivity', for characters, 768
    \sub for class functions, 768
    \sub for group actions, 401
  `TranslatorSubalgebra', 628
  transporter, 396
  `TransposedMat', 223
  `TransposedMatAttr', 223
  `TransposedMatDestructive', 223
  `TransposedMatImmutable', 223
  `TransposedMatMutable', 223
  `TransposedMatOp', 223
  `TransposedMatrixGroup', 424
  Transversals, \indexit{352}
  Triangular Matrices, \indexit{229}
  `TriangulizedIntegerMat', 237
  `TriangulizedIntegerMatTransform', 237
  `TriangulizedNullspaceMat', 225
  `TriangulizedNullspaceMatDestructive', 225
  `TriangulizeIntegerMat', 237
  `TriangulizeMat', 225
  `TrivialCharacter', 764
  `TrivialGroup', 503
  `TrivialIterator', 275
  `TrivialSubalgebra', 611
  `TrivialSubgroup', 357
  `TrivialSubmagmaWithOne', 319
  `TrivialSubmodule', 567
  `TrivialSubmonoid', 538
  `TrivialSubnearAdditiveMagmaWithZero', 552
  `TrivialSubspace', 590
  `TryCosetTableInWholeGroup', 465
  `TryGcdCancelExtRepPolynomials', 680
  `Tuples', 149
  tuple stabilizer, 396
  `TwoClosure', 421
  `TwoCoboundaries', 453
  `TwoCocycles', 453
  `TwoCohomology', 453
  `TwoGroup' library, 512
  `TwoSidedIdeal', 556
  `TwoSidedIdealByGenerators', 557
  `TwoSidedIdealNC', 557
  `TwoSquares', 142
  type, boolean, 167
    \sub cyclotomic, 155
    \sub records, 257
    \sub strings, 245
  `TypeObj', 125
  `TypeOfDefaultGeneralMapping', 309
  Types, \indexit{125}
  `TzEliminate', 486
  `TzFindCyclicJoins', 487
  `TzGo', 483
  `TzGoGo', 485
  `TzImagesOldGens', 491
  `TzInitGeneratorImages', 491
  `TzNewGenerator', 483
  `TzOptions', 496
  `TzPreImagesNewGens', 492
  `TzPrint', 482
  `TzPrintGeneratorImages', 492
  `TzPrintGenerators', 481
  `TzPrintLengths', 482
  `TzPrintOptions', 497
  `TzPrintPairs', 482
  `TzPrintPresentation', 482
  `TzPrintRelators', 481
  `TzPrintStatus', 482
  `TzSearch', 486
  `TzSearchEqual', 487
  `TzSort', 475
  `TzSubstitute', 488
  `TzSubstituteCyclicJoins', 491
\letter U
  $u_N$, 160
  `UglyVector', 602
  `Unbind', 43
    \sub for lists, 176
  `UnbindGlobal', 45
  `UnderlyingCharacteristic', 728
  `UnderlyingCharacterTable', 758
  `UnderlyingElement', fp group elements, 460
    \sub fp semigroup elements, 543
  `Underlying\-Element\-Of\-Rees\-Matrix\-Semigroup\-Element', 537
  `Underlying\-Element\-Of\-Rees\-Zero\-Matrix\-Semigroup\-Element', 537
  `UnderlyingExternalSet', 405
  `UnderlyingFamily', 631
  `UnderlyingGeneralMapping', 302
  `UnderlyingGroup', for character tables, 721
    \sub for tables of marks, 700
  `UnderlyingLeftModule', 593
  `UnderlyingLieAlgebra', 637
  `UnderlyingMagma', 654
  `UnderlyingRelation', 302
  `UnInstallCharReadHookFunc', 106
  `Union', 271
  union, of collections, 271
    \sub of sets, 194
  `Union2', 271
  `UnionBlist', 207
  `Unique', 195
  `UniteBlist', 208
  `UniteBlistList', 208
  `UniteSet', 194
  `Units', 560
  Units and Factorizations, \indexit{560}
  `UnivariatenessTestRationalFunction', 665
  `UnivariatePolynomial', 664
  `UnivariatePolynomialByCoefficients', 664
  `UnivariatePolynomialRing', 672
  Univariate Polynomial Rings, \indexit{672}
  Univariate Polynomials, \indexit{664}
  `Univariate\-Rational\-Function\-By\-Coefficients', 670
  Univariate Rational Functions, \indexit{670}
  `UniversalEnvelopingAlgebra', 643
  Universal Enveloping Algebras, \indexit{643}
  UNIX, features, 27
    \sub options, 27
  `UNIXSelect', 98
  `Unknown', 165
  `UnloadSmallGroupsData', 513
  `UnorderedTuples', 148
  Unpacking, \indexit{820}
  `UnprofileFunctions', 82
  `UnprofileMethods', 82
  `until', 52
  `UntraceMethods', 78
  `UpdateMap', 801
  `UpEnv', 70
  `UpperCentralSeriesOfGroup', 365
  `UpperSubdiagonal', 230
  `UseBasis', 568
  `UseFactorRelation', 293
  Useful Categories for all Elements of a Family, \indexit{296}
  Useful Categories of Elements, \indexit{294}
  `UseIsomorphismRelation', 293
  User Streams, \indexit{103}
  `UseSubsetRelation', 293
  utilities for editing GAP files, 74
\letter V
  $v_N$, 160
  `Valuation', 684
  `Value', 666
  `ValueCochain', 646
  `ValueGlobal', 44
  `ValueMolienSeries', 781
  `ValueOption', 88
  `ValuePol', 215
  `ValuesOfClassFunction', 758
  Variable Access in a Break Loop, \indexit{70}
  Variables, \indexit{42}
  Vectors as coefficients of polynomials, \indexit{215}
  `VectorSpace', 589
  `Vector\-Space\-By\-Pcgs\-Of\-Elementary\-Abelian\-Group', 443
  Vector Space Homomorphisms, \indexit{600}
  Vector Spaces Handled By Nice Bases, \indexit{602}
  `vi', 74
  `View', 65
  View and Print, \indexit{65}
  `ViewObj', 66
    \sub for character tables, 737
    \sub for class functions, 762
    \sub for tables of marks, 696
  `vim', 74
  `VirtualCharacter', 763
  virtual character, 765
  virtual characters, 756
\letter W
  $w_N$, 160
  `WedgeGModule ', 687
  `WeekDay', 255
  `WeightLexOrdering', 279
  `WeightOfGenerators', 280
  `WeightsTom', 702
  `WeightVecFFE', 214
  `WeylGroup', 638
  `WeylOrbitIterator', 640
  `Where', 70
  While, \indexit{51}
  `while' loop, 51
  Whitespaces, \indexit{40}
  Why Class Functions?, \indexit{756}
  `WordAlp', 250
  words, in generators, 348
  Working with large degree permutation groups, \indexit{421}
  `WreathProduct', 501
  wreath product embedding, 502
  `WreathProductImprimitiveAction', 501
  `WreathProductOrdering', 281
  `WreathProductProductAction', 502
  Wreath Products, \indexit{501}
  `WriteAll', 101
  `WriteByte', 101
  `WriteLine', 101
\letter X
  $x_N$, 160
\letter Y
  $y_N$, 160
\letter Z
  `Z', 576
  `ZClassRepsQClass', 428
  `Zero', 289
  `ZeroAttr', 289
  `ZeroCoefficient', 655
  `ZeroCoefficientRatFun', 679
  `ZeroImmutable', 289
  `ZeroMapping', 300
  `ZeroMutable', 289
  `ZeroOp', 289
  `ZeroSameMutability', 289
  `ZeroSM', 289
  `ZippedProduct', 680
  `ZippedSum', 680
  `ZmodnZ', 134
  `ZmodnZObj', 134
  `ZmodpZ', 134
  `ZmodpZNC', 134
  `ZumbroichBase', 585
  `Zuppos', 371
