\letter {}
  (Near-)Additive Magma Categories, \indexit{555}
  (Near-)Additive Magma Generation, \indexit{556}
  `+', 48
  `-', 48
  `-A', 30
  `-B', 30
  `-C', 31
  `-D', 30
  `-K', 29
  `-L', 29
  `-M', 30
  `-N', 30
  `-O', 30
  `-P', 31
    \sub on Macintosh, 31
  `-R', 29
  `-T', 31
  `-U', 31
  `-W', 31
    \sub on Macintosh, 32
  `-X', 31
  `-Y', 31
  `-a', 30
    \sub on Macintosh, 32
  `-b', 27
  `-e', 27
    \sub on Macintosh, 32
  `-f', 27
    \sub on Macintosh, 32
  `-g', 28
  `-g -g', 28
  `-h', 27
  `-i', 31
  `-l', 29
  `-m', 28
  `-n', 28
    \sub on Macintosh, 32
  `-o', 28
    \sub on Macintosh, 32
  `-p', 31
  `-q', 27
  `-r', 29
  `-x', 28
  `-y', 28
  `-z', 31
    \sub on Macintosh, 31
  `.gaprc', 33
  `/', 48
    \sub for character tables, 731
  `\*', 48
    \sub for character tables, 731
  `\\\char 39', 250
  `\\XYZ', 250
  `\\\"', 250
  `\\\\', 250
  `\\b', 250
  `\\c', 250
  `\\in', operation for testing membership, 274
  `\\n', 250
  `\\r', 250
  `{\accent 94 }', 48
    \sub for class functions, 769
  1-Cohomology, \indexit{377}
  2-Cohomology and Extensions, \indexit{456}
\letter A
  `AbelianGroup', 509
  `AbelianInvariants', for character tables, 733
    \sub for groups, 366
  Abelian Invariants for Subgroups, \indexit{476}
  `AbelianInvariantsMultiplier', 380
  `AbelianInvariantsNormalClosureFpGroup', 476
  `Abelian\-Invariants\-Normal\-Closure\-Fp\-Group\-Rrs', 476
  `AbelianInvariantsOfList', 242
  `AbelianInvariantsSubgroupFpGroup', 476
  `AbelianInvariantsSubgroupFpGroupMtc', 476
  `AbelianInvariantsSubgroupFpGroupRrs', 476
  `AbelianNumberField', 589
  abelian number field, 591
  abelian number fields, canonicalbasis, 592
  abelian number fields, Galois group, 594
  `AbelianSubfactorAction', 402
  About Group Actions, \indexit{394}
  `AbsInt', 127
  `AbsoluteIrreducibleModules', 750
  `AbsoluteValue', 159
  absolute value of an integer, 127
  `AbsolutIrreducibleModules', 750
  abstract word, 323
  `AbstractWordTietzeWord', 485
  accessing, list elements, 174
    \sub record elements, 260
  Accessing a Module, \indexit{695}
  Accessing Record Elements, \indexit{260}
  Accessing Subgroups via Tables of Marks, \indexit{716}
  `AClosestVectorCombinationsMatFFEVecFFE', 218
  `AClosest\-Vector\-Combinations\-Mat\-FFEVec\-FFECoords', 218
  `ActingAlgebra', 632
  `ActingDomain', 406
  Acting OnRight and OnLeft, \indexit{432}
  `Action', 401
  action, by conjugation, 395
    \sub on blocks, 395
    \sub on sets, 395
  `ActionHomomorphism', 400
  Action of a group on itself, \indexit{402}
  Action on Subfactors Defined by a Pcgs, \indexit{447}
  actions, 395
  Actions of Matrix Groups, \indexit{428}
  `ActorOfExternalSet', 408
  `Add', 177
  add, an element to a set, 196
  `AddCoeffs', 216
  `AddGenerator', 487
  `AddGenerators', 343
  `AddGeneratorsExtendSchreierTree', 424
  addition, 48
    \sub list and non-list, 185
    \sub matrices, 222
    \sub matrix and scalar, 222
    \sub operation, 294
    \sub rational functions, 668
    \sub scalar and matrix, 222
    \sub scalar and matrix list, 224
    \sub scalar and vector, 214
    \sub vector and scalar, 214
    \sub vectors, 214
  Additive Arithmetic for Lists, \indexit{185}
  `AdditiveInverse', 292
  `AdditiveInverseAttr', 292
  `AdditiveInverseImmutable', 292
  `AdditiveInverseMutable', 292
  `AdditiveInverseOp', 292
  `AdditiveInverseSameMutability', 292
  `AdditiveInverseSM', 292
  `AdditiveNeutralElement', 557
  `AddRelator', 487
  `AddRowVector', 216
  `AddRule', 343
  `AddRuleReduced', 343
  `AddSet', 196
  `AdjointAssociativeAlgebra', 649
  `AdjointBasis', 621
  `AdjointMatrix', 649
  `AdjointModule', 634
  Advanced Features of GAP, \indexit{30}
  Advanced List Manipulations, \indexit{205}
  Advanced Methods for Dixon-Schneider Calculations, \indexit{751}
  `AffineAction', 447
  `AffineActionLayer', 447
  `AffineOperation', 447
  `AffineOperationLayer', 447
  `Agemo', 363
  `Algebra', 612
  `AlgebraByStructureConstants', 615
  `AlgebraGeneralMappingByImages', 626
  `AlgebraHomomorphismByImages', 626
  `AlgebraHomomorphismByImagesNC', 626
  `AlgebraicExtension', 689
  `AlgebraWithOne', 612
  `AlgebraWithOneGeneralMappingByImages', 627
  `AlgebraWithOneHomomorphismByImages', 627
  `AlgebraWithOneHomomorphismByImagesNC', 627
  `AllBlocks', 405
  `AllIrreducibleSolvableGroups', 527
  `All<Library>Groups', 515
  `AllPrimitiveGroups', 515
  `AllSmallGroups', 518
  `AllTransitiveGroups', 515
  `Alpha', 821
  `AlternatingGroup', 509
  `and', 170
    \sub for filters, 117, 171
  An Example of Advanced Dixon-Schneider Calculations, \indexit{753}
  `ANFAutomorphism', 594
  `AntiSymmetricParts', 786
  antisymmetric relation, 313
  `Append', 178
  `AppendTo', 95
    \sub for streams, 101
  Apple, 837, 838
  `ApplicableMethod', 78
  ApplicableMethod, \indexit{78}
  `ApplicableMethodTypes', 78
  `Apply', 199
  `ApplySimpleReflection', 646
  `ApproximateSuborbitsStabilizerPermGroup', 422
  `ARCH_IS_MAC', 35
  `ARCH_IS_UNIX', 35
  `ARCH_IS_WINDOWS', 35
  `arg', special function argument, 46, 56
  Arithmetic for External Representations of Polynomials, \indexit{688}
  Arithmetic for Lists, \indexit{183}
  Arithmetic Operations for Class Functions, \indexit{768}
  Arithmetic Operations for Elements, \indexit{294}
  Arithmetic Operations for General Mappings, \indexit{307}
  Arithmetic Operators, \indexit{48}
  `Arrangements', 149
  arrow notation for functions, 57
  `AsAlgebra', 621
  `AsAlgebraWithOne', 622
  `AsBinaryRelationOnPoints', 314
  `AsBlockMatrix', 238
  `AscendingChain', 369
  `AsDivisionRing', 576
  `AsDuplicateFreeList', 198
  `AsField', 576
  `AsFreeLeftModule', 573
  `AsGroup', 348
  `AsGroupGeneralMappingByImages', 384
  `AsLeftIdeal', 563
  `AsLeftModule', 571
  `AsList', 269
  `AsMagma', 318
  `AsMonoid', 543
  `AsPolynomial', 670
  `AsRightIdeal', 563
  `AsRing', 560
  `AsSemigroup', 536
  `Assert', 81
  `AssertionLevel', 81
  Assertions, \indexit{81}
  `AsSet', 269
  `AssignGeneratorVariables', 330
  assignment, to a list, 176
    \sub to a record, 260
    \sub variable, 50
  Assignments, \indexit{50}
  `AssignNiceMonomorphismAutomorphismGroup', 390
  `AssociatedPartition', 154
  `AssociatedReesMatrixSemigroupOfDClass', 542
  `Associates', 566
  associativity, 48
  `AssocWordByLetterRep', 335
  `AsSortedList', 269
  `AsSSortedList', 269
  `As<Struct>', 286
  `AsSubalgebra', 622
  `AsSubalgebraWithOne', 622
  `AsSubgroup', 349
  `AsSubgroupOfWholeGroupByQuotient', 474
  `AsSubmagma', 319
  `AsSubmonoid', 543
  `AsSubsemigroup', 536
  `AsSubspace', 597
  `AsSub<struct>', 289
  `AsTransformation', 553
  `AsTransformationNC', 553
  `AsTwoSidedIdeal', 563
  `AsVectorSpace', 596
  at exit functions, 73
  ATLAS Irrationalities, \indexit{161}
  `AtlasIrrationality', 163
  atomic irrationalities, 161
  Attributes, \indexit{121}
  Attributes and Operations for Algebras, \indexit{620}
  Attributes and Properties for (Near-)Additive Magmas, \indexit{557}
  Attributes and Properties for Collections, \indexit{270}
  Attributes and Properties for Magmas, \indexit{320}
  Attributes and Properties for Matrix Groups, \indexit{427}
  Attributes and Properties of Character Tables, \indexit{731}
  Attributes and Properties of Elements, \indexit{290}
  Attributes of and Operations on Equivalence Relations, \indexit{315}
  Attributes of Tables of Marks, \indexit{706}
  `AttributeValueNotSet', 122
  `AugmentationIdeal', 661
  `AugmentedCosetTableInWholeGroup', 468
  `AugmentedCosetTableMtc', 468
  `AugmentedCosetTableRrs', 468
  Augmented Coset Tables and Rewriting, \indexit{468}
  automatic loading of gap packages, 842
  `AutomorphismDomain', 389
  `AutomorphismGroup', 389
    \sub for groups with pcgs, 448
  automorphism group, of number fields, 594
  Automorphisms and Equivalence of Character Tables, \indexit{760}
  `AutomorphismsOfTable', 734
\letter B
  $b_N$, 161
  backslash character, 250
  backspace character, 250
  `Backtrace', GAP3 name for `Where', 70
  Backtrack, \indexit{424}
  `BANNER', 847
  `BaseFixedSpace', 229
  `BaseIntersectionIntMats', 239
  `BaseIntMat', 239
  `BaseMat', 232
  `BaseMatDestructive', 232
  `BaseOfGroup', 421
  `BaseOrthogonalSpaceMat', 232
  Bases of Vector Spaces, \indexit{598}
  `BaseStabChain', 421
  `BaseSteinitzVectors', 232
  Basic Actions, \indexit{395}
  Basic Groups, \indexit{508}
  Basic Operations for Class Functions, \indexit{766}
  Basic Operations for Lists, \indexit{174}
  `BasicWreathProductOrdering', 282
  `Basis', 599
  `BasisNC', 599
  `BasisVectors', 600
  `Bell', 148
  `Bernoulli', 148
  `BestQuoInt', 129
  `BestSplittingMatrix', 752
  `BiAlgebraModule', 630
  `BiAlgebraModuleByGenerators', 630
  `BilinearFormMat', 645
  binary relation, 312
  `BinaryRelationByElements', 312
  `BinaryRelationOnPoints', 314
  `BinaryRelationOnPointsNC', 314
  Binary Relations on Points, \indexit{314}
  `BinaryRelationTransformation', 554
  `BindGlobal', 45
  `Binomial', 147
  blank, 41
  `BlistList', 209
  Block Matrices, \indexit{238}
  `BlockMatrix', 238
  `Blocks', 405
  `BlocksInfo', 739
  Block Systems, \indexit{405}
  `BlownUpMat', 234
  `BlownUpVector', 234
  `BlowUpIsomorphism', 428
  BNF, 59
  body, 55
  `BombieriNorm', 676
  Boolean Lists Representing Subsets, \indexit{209}
  bound, 43
  Brauer character, 773
  `BrauerCharacterValue', 796
  `BrauerTable', 725
  `BrauerTableOp', 725
  `BravaisGroup', 431
  `BravaisSubgroups', 431
  `BravaisSupergroups', 431
  Break, \indexit{55}
  break loop message, 70
  Break Loops, \indexit{67}
  `break' statement, 55
  browsing backwards, 22
  browsing backwards one chapter, 23
  browsing forward, 22
  browsing forward one chapter, 23
  browsing the next section browsed, 23
  browsing the previous section browsed, 23
  Browsing through the Sections, \indexit{22}
  bug reports, see If Things Go Wrong, 834
  Building new orderings, \indexit{278}
\letter C
  $c_N$, 161
  Calculating with Group Automorphisms, \indexit{390}
  Calendar Arithmetic, \indexit{257}
  `CallFuncList', 62
  Calling a function with a list argument that is interpreted as several arguments, \indexit{62}
  Cancellation Tests for Rational Functions, \indexit{688}
  `CanComputeIndex', 381
  `CanComputeIsSubset', 381
  `CanComputeSize', 381
  `CanComputeSizeAnySubgroup', 381
  candidates, for permutation characters, 789, 792
  `CanEasilyCompareElements', 293
  `CanEasilyCompareElementsFamily', 293
  `CanEasilyComputePcgs', 434
  `CanEasilySortElements', 293
  `CanEasilySortElementsFamily', 293
  `CanEasilyTestMembership', 381
  `CanonicalBasis', 599
  canonical basis, for matrix spaces, 606
    \sub for row spaces, 606
  `CanonicalGenerators', 645
  `CanonicalPcElement', 436
  `CanonicalPcgs', 439
  `CanonicalPcgsByGeneratorsWithImages', 441
  `Canonical\-Representative\-Determinator\-Of\-External\-Set', 408
  `CanonicalRepresentativeOfExternalSet', 408
  `CanonicalRightCosetElement', 355
  Carmichael's lambda function, 139
  carriage return character, 250
  `CartanMatrix', 644
  `CartanSubalgebra', 641
  `Cartesian', 200
  Categories, \indexit{118}
  Categories and Properties of Algebras, \indexit{619}
  Categories for Streams and the StreamsFamily, \indexit{97}
  Categories of Associative Words, \indexit{328}
  Categories of Matrices, \indexit{221}
  `CategoriesOfObject', 120
  Categories of Words and Nonassociative Words, \indexit{323}
  `CategoryCollections', 266
  `Center', 321
  center, 320
  `CentralCharacter', 776
  central character, 776
  `CentralIdempotentsOfAlgebra', 624
  centraliser, 320
  `Centralizer', 320
    \sub for groups with pcgs, 448
  `CentralizerInGLnZ', 431
  `CentralizerModulo', 370
  `CentralizerSizeLimitConsiderFunction', 449
  `CentralNormalSeriesByPcgs', 443
  `Centre', 321
    \sub for groups with pcgs, 448
  centre, of a character, 775
  `CentreOfCharacter', 775
  `CF', 589
  `ChangeStabChain', 423
  Changing Presentations, \indexit{487}
  Changing the Help Viewer, \indexit{23}
  Changing the Representation, \indexit{287}
  Changing the Structure, \indexit{286}
  `CHAR_INT', 255
  `CHAR_SINT', 256
  `Character', 771
  Character Conversion, \indexit{255}
  `CharacterDegrees', 731
  Character Degrees and Derived Length, \indexit{821}
  `Characteristic', 290
  characteristic, for class functions, 770
  `CharacteristicPolynomial', 233
  characteristic polynomial, for field elements, 578
  `CharacterNames', 735
  characters, 764
    \sub permutation, 789, 792
    \sub symmetrizations of, 785
  `CharacterTable', 725
  Character Table Categories, \indexit{727}
  `CharacterTableDirectProduct', 755
  `CharacterTableFactorGroup', 755
  `CharacterTableIsoclinic', 756
  character tables, 724
    \sub access to, 724
    \sub calculate, 724
    \sub infix operators, 731
    \sub of groups, 724
  `CharacterTableWithSortedCharacters', 757
  `CharacterTableWithSortedClasses', 758
  `CharacterTableWreathSymmetric', 757
  character value, of group element using powering operator, 769
  `CharsFamily', 251
  `CheapFactorsInt', 134
  `CheckFixedPoints', 810
  `CheckForHandlingByNiceBasis', 611
  `CheckPermChar', 817
  `ChevalleyBasis', 643
  `ChiefNormalSeriesByPcgs', 444
  `ChiefSeries', 367
  `ChiefSeriesThrough', 367
  `ChiefSeriesUnderAction', 367
  `ChineseRem', 130
  Chinese remainder, 131
  `Chomp', 255
  `CIUnivPols', 668
  `ClassElementLattice', 372
  classes, real, 736
  `ClassesSolvableGroup', 448
  `ClassFunction', 771
  class function, 764
  class function objects, 764
  class functions, 807
    \sub as ring elements, 768
  `ClassFunctionSameType', 772
  Class Fusions between Character Tables, \indexit{802}
  Classical Groups, \indexit{510}
  `ClassMultiplicationCoefficient', for character tables, 743
  class multiplication coefficient, 743, 744
  `ClassNames', 735
  `ClassNamesTom', 707
  `ClassOrbit', 736
  `ClassPermutation', 759
  `ClassPositionsOfAgemo', 737
  `ClassPositionsOfCentre', for characters, 775
    \sub for character tables, 737
  `ClassPositionsOfDerivedSubgroup', 737
  `Class\-Positions\-Of\-Direct\-Product\-Decompositions', 737
  `ClassPositionsOfElementaryAbelianSeries', 737
  `ClassPositionsOfFittingSubgroup', 737
  `ClassPositionsOfKernel', 775
  `ClassPositionsOfLowerCentralSeries', 737
  `ClassPositionsOfMaximalNormalSubgroups', 737
  `ClassPositionsOfMinimalNormalSubgroups', 737
  `ClassPositionsOfNormalClosure', 738
  `ClassPositionsOfNormalSubgroup', 762
  `ClassPositionsOfNormalSubgroups', 737
  `ClassPositionsOfSupersolvableResiduum', 738
  `ClassPositionsOfUpperCentralSeries', 737
  `ClassRoots', 736
  `ClassStructureCharTable', 744
  `ClassTypesTom', 706
  `CleanedTailPcElement', 437
  `ClearCacheStats', 84
  `ClearProfile', 83
  clone, an object, 114
  `CloseMutableBasis', 604
  `CloseStream', 98
  `ClosureGroup', 351
  `ClosureGroupAddElm', 351
  `ClosureGroupCompare', 351
  `ClosureGroupDefault', 351
  `ClosureGroupIntest', 351
  `ClosureLeftModule', 572
  `ClosureNearAdditiveGroup', 558
  Closure Operations and Other Constructors, \indexit{314}
  `ClosureRing', 560
  Closures of (Sub)groups, \indexit{351}
  `Closure<Struct>', 286
  `ClosureSubgroup', 351
  `ClosureSubgroupNC', 351
  `Coboundaries', 654
  `Cochain', 653
  `CochainSpace', 653
  `Cocycles', 654
  cocycles, 377
  `CodePcGroup', 459
  `CodePcgs', 459
  Coding a Pc Presentation, \indexit{459}
  coefficient, binomial, 147
  Coefficient List Arithmetic, \indexit{216}
  `Coefficients', 600
  coefficients, for cyclotomics, 159
  `CoefficientsAndMagmaElements', 662
  `CoefficientsFamily', 685
  `CoefficientsMultiadic', 130
  `CoefficientsOfLaurentPolynomial', 677
  `CoefficientsOfUnivariatePolynomial', 670
  `Coefficients\-Of\-Univariate\-Rational\-Function', 670
  `CoefficientsQadic', 130
  `CoefficientsRing', 678
  `CoeffsCyc', 159
  `CoeffsMod', 217
  cohomology, 377
  `COHORTS_PRIMITIVE_GROUPS', 525
  `CoKernelOfAdditiveGeneralMapping', 309
  `CoKernelOfMultiplicativeGeneralMapping', 308
  `CollapsedMat', 813
  `Collected', 198
  Collection Families, \indexit{265}
  `CollectionsFamily', 265
  Coloring the Prompt and Input, \indexit{38}
  `ColorPrompt', 38
  `ColumnIndexOfReesMatrixSemigroupElement', 542
  `Column\-Index\-Of\-Rees\-Zero\-Matrix\-Semigroup\-Element', 542
  `Combinations', 149
  Combinations, Arrangements and Tuples, \indexit{149}
  `CombinatorialCollector', 453
  Combinatorial Numbers, \indexit{147}
  `Comm', 294
    \sub for words, 332
  Command Line Options, \indexit{27}
  comments, 41
  `CommutativeDiagram', 810
  `CommutatorFactorGroup', 370
  `CommutatorLength', 361
    \sub for character tables, 733
  `CommutatorSubgroup', 360
  `Compacted', 198
  `CompanionMat', 235
  `CompareVersionNumbers', 845
  comparison, fp semigroup elements, 548
    \sub operation, 293
    \sub rational functions, 668
  Comparison of Associative Words, \indexit{331}
  Comparison of Class Functions, \indexit{767}
  Comparison of Elements of Finitely Presented Groups, \indexit{462}
  Comparison of Elements of Finitely Presented Semigroups, \indexit{548}
  Comparison of Permutations, \indexit{410}
  Comparison of Rational Functions, \indexit{668}
  Comparison of Words, \indexit{325}
  Comparison Operations for Elements, \indexit{293}
  Comparisons, \indexit{47}
  comparisons, of booleans, 169
    \sub of lists, 182
  Comparisons of Booleans, \indexit{169}
  Comparisons of Cyclotomics, \indexit{161}
  Comparisons of Lists, \indexit{182}
  Comparisons of Records, \indexit{262}
  Comparisons of Strings, \indexit{252}
  `CompatibleConjugacyClasses', 729
  `CompatiblePairs', 457
  Compilation, \indexit{829}
  Compiling Library Code, \indexit{36}
  `Complementclasses', 360
  `ComplementclassesEA', 379
  `ComplementIntMat', 240
  `ComplementSystem', 363
  Completion Files, \indexit{34}
  `ComplexConjugate', 164
    \sub for class functions, 770
  `ComplexificationQuat', 616
  Components of a Dixon Record, \indexit{752}
  `CompositionMapping', 302
    \sub for Frobenius automorphisms, 586
  `CompositionMapping2', 302
  `CompositionMaps', 807
  `CompositionOfStraightLinePrograms', 339
  `CompositionSeries', 367
    \sub for groups with pcgs, 448
  `ComputedBrauerTables', 725
  `ComputedClassFusions', 803
  `ComputedIndicators', 743
  `ComputedIsPSolvableCharacterTables', 742
  `ComputedPowerMaps', 799
  `ComputedPrimeBlockss', 738
  Computing a Pcgs, \indexit{434}
  Computing a Permutation Representation, \indexit{414}
  Computing Pc Groups, \indexit{454}
  Computing Possible Permutation Characters, \indexit{792}
  Computing the Irreducible Characters of a Group, \indexit{748}
  `Concatenation', 197
  concatenation, of lists, 198
  `Conductor', 159
  `ConfluentRws', 343
  `Congruences', for character tables, 815
  Congruences for semigroups, \indexit{539}
  `ConjugacyClass', 357
  Conjugacy Classes, \indexit{357}
  `ConjugacyClasses', attribute, 357
    \sub for character tables, 728
    \sub for groups with pcgs, 448
    \sub for linear groups, 514
  `ConjugacyClassesByOrbits', 358
  `ConjugacyClassesByRandomSearch', 358
  Conjugacy Classes in Classical Groups, \indexit{514}
  Conjugacy Classes in Solvable Groups, \indexit{448}
  `ConjugacyClassesMaximalSubgroups', 371
  `ConjugacyClassesPerfectSubgroups', 374
  `ConjugacyClassesSubgroups', 371
  `ConjugacyClassSubgroups', 371
  conjugate, matrix, 223
    \sub of a word, 332
  `ConjugateDominantWeight', 646
  `ConjugateDominantWeightWithWord', 646
  `ConjugateGroup', 348
  `Conjugates', 579
  `ConjugateSubgroup', 350
  `ConjugateSubgroups', 350
  conjugation, 395
  `ConjugatorAutomorphism', 388
  `ConjugatorAutomorphismNC', 388
  `ConjugatorIsomorphism', 387
  `ConjugatorOfConjugatorIsomorphism', 388
  `ConnectGroupAndCharacterTable', 729
  `ConsiderKernels', 815
  `ConsiderSmallerPowerMaps', 816
  `ConsiderStructureConstants', 807
  `ConsiderTableAutomorphisms', 818
  `ConstantTimeAccessList', 194
  constituent, of a group character, 774
  `ConstituentsCompositionMapping', 303
  `ConstituentsOfCharacter', 775
  Constructing Algebras as Free Algebras, \indexit{613}
  Constructing Algebras by Generators, \indexit{612}
  Constructing Algebras by Structure Constants, \indexit{614}
  Constructing Character Tables from Others, \indexit{754}
  Constructing Domains, \indexit{285}
  Constructing Lie algebras, \indexit{638}
  Constructing Pc Groups, \indexit{452}
  Constructing Subdomains, \indexit{289}
  Constructing Tables of Marks, \indexit{701}
  Constructing Vector Spaces, \indexit{596}
  Construction of Abelian Number Fields, \indexit{589}
  Construction of Stabilizer Chains, \indexit{419}
  Constructors for Basic Groups, \indexit{514}
  `ContainedCharacters', 814
  `ContainedDecomposables', 814
  `ContainedMaps', 809
  `ContainedPossibleCharacters', 812, 813
  `ContainedPossibleVirtualCharacters', 812, 813
  `ContainedSpecialVectors', 812, 813
  `ContainedTom', 711
  `ContainingTom', 711
  `ContinuedFractionApproximationOfRoot', 143
  `ContinuedFractionExpansionOfRoot', 143
  Continued Fractions, \indexit{143}
  `continue' statement, 55
  Conventions for Character Tables, \indexit{728}
  convert, to a string, 251
  Converting Groups to Finitely Presented Groups, \indexit{470}
  `ConvertToCharacterTable', 726
  `ConvertToCharacterTableNC', 726
  `ConvertToMatrixRep', 235
  `ConvertToMatrixRepNC', 235
  `ConvertToRangeRep', 207
  `ConvertToStringRep', 251
  `ConvertToTableOfMarks', 705
  `ConvertToVectorRep', 215
  `ConvertToVectorRepNC', 215
  `ConwayPolynomial', 586
  Conway Polynomials, \indexit{586}
  coprime, 48
  copy, 114
    \sub an object, 114
  `COPY_LIST_ENTRIES', 178
  `CopyOptionsDefaults', 423
  Copyrights, \indexit{841}
  `CopyStabChain', 423
  `Core', 359
  `CorrespondingGeneratorsByModuloPcgs', 441
  coset, 354
  `CosetLeadersMatFFE', 218
  Cosets, \indexit{354}
  `CosetTable', 464
  `CosetTableBySubgroup', 465
  `CosetTableDefaultLimit', 466
  `CosetTableDefaultMaxLimit', 466
  `CosetTableFromGensAndRels', 465
  `CosetTableInWholeGroup', 468
  `CosetTableOfFpSemigroup', 551
  Coset Tables and Coset Enumeration, \indexit{464}
  Coset tables for subgroups in the whole group, \indexit{468}
  `CosetTableStandard', 467
  CRC, 37
  `CrcFile', 95
    \sub example, 37
  CRC Numbers, \indexit{37}
  `CreateCompletionFiles', 34
  `CreateCompletionFilesPkg', 846
  Creating Character Tables, \indexit{724}
  Creating Class Functions from Values Lists, \indexit{771}
  Creating Class Functions using Groups, \indexit{772}
  Creating Finite Fields, \indexit{584}
  Creating Finitely Presented Groups, \indexit{461}
  Creating Finitely Presented Semigroups, \indexit{547}
  Creating Group Homomorphisms, \indexit{382}
  Creating Groups, \indexit{347}
  Creating Mappings, \indexit{302}
  Creating Permutations, \indexit{412}
  Creating Presentations, \indexit{479}
  Creation of Algebraic Extensions, \indexit{689}
  Creation of Rational Functions, \indexit{687}
  Credit, \indexit{21}
  `CrystGroupDefaultAction', 432
  `Cycle', 403
  `CycleLength', 403
  `CycleLengths', 403
  `Cycles', 403
  `CycleStructureClass', 776
  `CycleStructurePerm', 411
  `CyclicExtensionsTom', 711
  `CyclicGroup', 508
  `CyclotomicField', 589
  cyclotomic field elements, 157
  cyclotomic fields, canonicalbasis, 592
  `CyclotomicPolynomial', 674
  Cyclotomic Polynomials, \indexit{674}
  `Cyclotomics', 157
  cyclotomics, defaultfield, 590
\letter D
  $d_N$, 161
  Darstellungsgruppe, see `EpimorphismSchurCover', 380
  `DataType', 125
  data type, unknown, 167
  `DayDMY', 257
  `DaysInMonth', 257
  `DaysInYear', 257
  Debugging Recursion, \indexit{85}
  DEC, 243
  `DeclareAutoPackage', 846
  `DeclareHandlingByNiceBasis', 610
  `DeclareInfoClass', 80
  `DeclarePackage', 846
  `DeclarePackageAutoDocumentation', 846
  `DeclarePackageDocumentation', 846
  `DecodeTree', 497
  DecodeTree, \indexit{497}
  decompose, a group character, 774
  `DecomposedFixedPointVector', 711
  `DecomposeTensorProduct', 655
  `Decomposition', 243
  `DecompositionInt', 244
  `DecompositionMatrix', 740
  decomposition matrix, 243
  Decompositions, \indexit{243}
  `Decreased', 783
  `DefaultField', 576
    \sub for cyclotomics, 160
    \sub for finite field elements, 584
  `DefaultFieldByGenerators', 576
  `DefaultFieldOfMatrix', 224
  `DefaultFieldOfMatrixGroup', 427
  `DefaultRing', 559
    \sub for finite field elements, 584
  `DefaultRingByGenerators', 560
  `DefaultStabChainOptions', 420
  Defining a Pcgs Yourself, \indexit{434}
  `DefiningPolynomial', 577
  `DefiningQuotientHomomorphism', 474
  `DegreeFFE', 583
  `DegreeIndeterminate', 672
  `DegreeOfBinaryRelation', 313
  `DegreeOfCharacter', 774
  `DegreeOfLaurentPolynomial', 671
  `DegreeOfTransformation', 552
  `DegreeOfTransformationSemigroup', 538
  `DegreeOverPrimeField', 577
  `Delta', 821
  denominator, of a rational, 146
  `DenominatorCyc', 160
  `DenominatorOfModuloPcgs', 440
  `DenominatorOfRationalFunction', 670
  `DenominatorRat', 146
  deprecated, 846
  `DepthOfPcElement', 436
  `DepthOfUpperTriangularMatrix', 233
  `Derangements', 151
  `Derivations', 639
  `Derivative', 673
  `DerivedLength', 368
  `DerivedSeriesOfGroup', 368
  `DerivedSubgroup', 360
  `DerivedSubgroupsTom', 710
  `DerivedSubgroupsTomPossible', 710
  `DerivedSubgroupsTomUnique', 710
  `DerivedSubgroupTom', 710
  `DescriptionOfRootOfUnity', 160
  `Determinant', 225
  determinant character, 776
  `DeterminantIntMat', 243
  `DeterminantMat', 225
  `DeterminantMatDestructive', 225
  `DeterminantMatDivFree', 225
  Determinant of an integer matrix, \indexit{243}
  `DeterminantOfCharacter', 776
  Developing rewriting systems, \indexit{345}
  `DiagonalizeIntMat', 241
  `DiagonalizeMat', 230
  `DiagonalMat', 226
  `DiagonalOfMat', 233
  `Difference', 273
  `DifferenceBlist', 210
  `DihedralGroup', 509
  `Dimension', 573
  `DimensionOfHighestWeightModule', 655
  `DimensionOfMatrixGroup', 427
  `DimensionOfVectors', 605
  `DimensionsLoewyFactors', 369
  `DimensionsMat', 224
  Directories, \indexit{91}
  `DirectoriesLibrary', 91
  `DirectoriesPackageLibrary', 844
  `DirectoriesPackagePrograms', 845
  `DirectoriesSystemPrograms', 92
  `Directory', 91
  `DirectoryContents', 92
  `DirectoryCurrent', 91
  `DirectoryTemporary', 91
  `DirectProduct', 502
  `DirectProductOp', 502
  Direct Products, \indexit{502}
  `DirectSumDecomposition', 624
    \sub for Lie algebras, 643
  Direct Sum Decompositions, \indexit{643}
  `DirectSumOfAlgebraModules', 635
    \sub for Lie algebras, 658
  `DirectSumOfAlgebras', 623
  `DisableAttributeValueStoring', 123
  disable automatic loading, 842
  `Discriminant', 673
  `Display', 67
    \sub for character tables, 744, 771
    \sub for tables of marks, 703
  `DisplayCacheStats', 84
  `DisplayCompositionSeries', 367
  `DisplayEggBoxOfDClass', 540
  `DisplayImfInvariants', 529
  `DisplayInformationPerfectGroups', 522
  `DisplayOptions', 746
  `DisplayOptionsStack', 89
  `DisplayProfile', 83
  `DisplayRevision', 84
  `DistancesDistributionMatFFEVecFFE', 218
  `DistancesDistributionVecFFEsVecFFE', 218
  `DistanceVecFFE', 218
  Distinguished Subalgebras, \indexit{640}
  division, 48
    \sub operation, 294
  `DivisionRingByGenerators', 576
  division rings, 575
  divisors, of an integer, 134
  `DivisorsInt', 134
  Dixon-Schneider algorithm, 751
  `DixonInit', 751
  `DixonRecord', 751
  `DixonSplit', 752
  `DixontinI', 751
  `DMYDay', 257
  `DMYhmsSeconds', 258
  `DnLattice', 784
  `DnLatticeIterative', 785
  `do', 53
  document formats (text, dvi, ps, pdf, html), 23
  `Domain', 290
  `DomainByGenerators', 290
  Domain Categories, \indexit{287}
  Domains, \indexit{111}
  Domains Generated by Class Functions, \indexit{797}
  Domains of Subspaces of Vector Spaces, \indexit{598}
  `DominantCharacter', 654
  `DominantWeights', 654
  `DoubleCoset', 356
  `DoubleCosetRepsAndSizes', 357
  Double Cosets, \indexit{356}
  `DoubleCosets', operation, 356
  `DoubleCosetsNC', operation, 356
  doublequote character, 250
  doublequotes, 248
  `DownEnv', 71
  Dummy Streams, \indexit{106}
  duplicate free, 193
  `DuplicateFreeList', 198
  Duplication of Lists, \indexit{180}
  Duplication of Objects, \indexit{114}
  `DxIncludeIrreducibles', 752
\letter E
  `E', 157
  $e_N$, 161
  `EANormalSeriesByPcgs', 442
  `Earns', 404
  `EB', 161
  `EC', 161
  Echelonized Matrices, \indexit{230}
  `ED', 161
  `Edit', 75
  Editing Files, \indexit{75}
  Editor Support, \indexit{75}
  `EE', 161
  `EF', 161
  Efficiency of Homomorphisms, \indexit{385}
  `EG', 161
  `EggBoxOfDClass', 540
  `EH', 161
  `EI', 162
  `Eigenspaces', 229
  `Eigenvalues', 229
  `EigenvaluesChar', 777
  `Eigenvectors', 229
  Eigenvectors and eigenvalues, \indexit{229}
  `EJ', 162
  `EK', 162
  `EL', 162
  `ElementaryAbelianGroup', 509
  `ElementaryAbelianSeries', 368
  `ElementaryAbelianSeriesLargeSteps', 368
  Elementary Divisors, \indexit{230}
  `ElementaryDivisorsMat', 230
  `ElementaryDivisorsMatDestructive', 230
  Elementary Operations for a Pcgs, \indexit{435}
  Elementary Operations for a Pcgs and an Element, \indexit{436}
  Elementary Operations for Integers, \indexit{127}
  Elementary Operations for Rationals, \indexit{145}
  Elementary Tietze Transformations, \indexit{490}
  `ElementOfFpGroup', 463
  `ElementOfFpSemigroup', 549
  `ElementOfMagmaRing', 662
  `ElementOrdersPowerMap', 800
  `ElementProperty', 424
  `Elements', 270
  elements, definition, 110
    \sub of a list or collection, 270
  Elements as equivalence classes, \indexit{110}
  `ElementsFamily', 265
  Elements in Algebraic Extensions, \indexit{689}
  Elements of Free Magma Rings, \indexit{662}
  Elements of pc groups, \indexit{451}
  `ElementsStabChain', 422
  Elements with Prescribed Images, \indexit{400}
  element test, for lists, 182
  `elif', 51
  `EliminatedWord', 333
  `EliminationOrdering', 682
  `else', 51
  `EM', 162
  `emacs', 75
  `Embedding', 303
    \sub example for direct products, 502
    \sub example for semidirect products, 504
    \sub example for wreath products, 505
    \sub for group products, 507
    \sub for Lie algebras, 638
    \sub for magma rings, 662
  embeddings, find all, 391
  Embeddings and Projections for Group Products, \indexit{507}
  `EmptyBinaryRelation', 312
  `EmptyMatrix', 226
  `EmptySCTable', 614
  `EmptyStabChain', 423
  `EnableAttributeValueStoring', 123
  `End', 608
  `end', 55
  Enlarging Internally Represented Lists, \indexit{182}
  `Enumerator', 266
  `EnumeratorByBasis', 601
  `EnumeratorByFunctions', 267
  Enumerators, \indexit{208}
  `EnumeratorSorted', 266
  environment, 55
  `Epicentre', 380
  `EpimorphismFromFreeGroup', 351
  `EpimorphismNilpotentQuotient', 475
  `EpimorphismNonabelianExteriorSquare', 380
  `EpimorphismPGroup', 475
  `EpimorphismQuotientSystem', 475
  epimorphisms, find all, 391
  `EpimorphismSchurCover', 380
  equality, associative words, 331
    \sub elements of finitely presented groups, 462
    \sub nonassociative words, 325
    \sub of records, 262
    \sub operation, 293
    \sub pcwords, 451
  Equality and Comparison of Domains, \indexit{285}
  equality test, 47
    \sub for permutations, 410
  equivalence class, 316
  Equivalence Classes, \indexit{316}
  `EquivalenceClasses', attribute, 316
  `EquivalenceClassOfElement', 316
  `EquivalenceClassOfElementNC', 316
  `EquivalenceClassRelation', 316
  equivalence relation, 313, 315
  `EquivalenceRelationByPairs', 315
  `EquivalenceRelationByPairsNC', 315
  `EquivalenceRelationByPartition', 315
  `EquivalenceRelationByPartitionNC', 315
  `EquivalenceRelationByProperty', 315
  `EquivalenceRelationByRelation', 315
  `EquivalenceRelationPartition', 315
  Equivalence Relations, \indexit{315}
  `ER', 162
  `Error', 73
  Error, \indexit{73}
  `ErrorCount', 73
  ErrorCount, \indexit{73}
  `ErrorNoTraceBack', 69
  errors, syntax, 64
  `ES', 162
  escaped characters, 250
  escaping non-special characters, 250
  `ET', 162
  `EU', 162
  `EuclideanDegree', 567
  `EuclideanQuotient', 567
  `EuclideanRemainder', 568
  Euclidean Rings, \indexit{567}
  Euler's totient function, 138
  `EulerianFunction', 366
  `EulerianFunctionByTom', 712
  `EV', 162
  `EvalStraightLineProgElm', 341
  `EvalString', 257
  evaluation, 42
    \sub strings, 256
  `EW', 162
  `EX', 162
  `ExactSizeConsiderFunction', 376
  `Exec', 109
  Exec, \indexit{109}
  execution, 49
  exit, 73
  expanded form of monomials, 686
  Expert Windows installation, \indexit{840}
  `Exponent', 366
    \sub for character tables, 733
  exponent, of the prime residue group, 139
  exponentiation, operation, 294
  `ExponentOfPcElement', 436
  `ExponentsConjugateLayer', 437
  `ExponentsOfCommutator', 437
  `ExponentsOfConjugate', 437
  `ExponentsOfPcElement', 436
  `ExponentsOfRelativePower', 437
  Exponents of Special Products, \indexit{437}
  `ExponentSumWord', 332
  `ExponentSyllable', 334
  Expressing Group Elements as Words in Generators, \indexit{351}
  Expressions, \indexit{42}
  `ExtendedPcgs', 439
  `ExtendStabChain', 423
  `Extension', 456
  `ExtensionNC', 456
  `ExtensionRepresentatives', 457
  `Extensions', 456
  Extensions of the p-adic Numbers, \indexit{692}
  `ExteriorCentre', 380
  `ExteriorPowerOfAlgebraModule', 658
  `ExternalOrbit', 407
  `ExternalOrbits', 407
  `ExternalOrbitsStabilizers', 407
  External Representation for Nonassociative Words, \indexit{327}
  external representation of polynomials, 686
  `ExternalSet', 406
  External Sets, \indexit{406}
  `ExternalSubset', 407
  `Extract', 781
  `ExtraspecialGroup', 509
  `ExtRepDenominatorRatFun', 686
  `ExtRepNumeratorRatFun', 686
  `ExtRepOfObj', external representation, for cyclotomics, 160
  `ExtRepPolynomialRatFun', 686
  `EY', 162
\letter F
  $f_N$, 161
  `FactorCosetAction', 402
    \sub for fp groups, 465
  `FactorCosetOperation', 465
  `FactorFreeSemigroupByRelations', 547
  `FactorGroup', 370
  `FactorGroupFpGroupByRels', 461
  `FactorGroupNC', 370
  `FactorGroupNormalSubgroupClasses', 762
  Factor Groups, \indexit{370}
  Factor Groups of Polycyclic Groups - Modulo Pcgs, \indexit{440}
  Factor Groups of Polycyclic Groups in their Own Representation, \indexit{441}
  `FactorGroupTom', 712
  `Factorial', 147
  `Factorization', 352
  factorization, 351
  `Factors', 567
    \sub of univariate polynomial, 675
  `FactorsInt', 132
  `FactorsOfDirectProduct', 755
  `FactorsSquarefree', 675
  Fail, \indexit{169}
  `fail', 169
  `FaithfulModule', 634
    \sub for Lie algebras, 652
  Families, \indexit{116}
  `FamiliesOfGeneralMappingsAndRanges', 311
  `FamiliesOfRows', 761
  `FamilyForOrdering', 279
  `FamilyObj', 116
  `FamilyPcgs', 451
  `FamilyRange', 311
  `FamilySource', 311
  FAQ, 833
  features, under UNIX, 27
  `fi', 51
  `Fibonacci', 155
  Fibonacci and Lucas Sequences, \indexit{155}
  `Field', 575
  `FieldExtension', 577
  field homomorphisms, Frobenius, 586
  `FieldOfMatrixGroup', 427
  `FieldOverItselfByGenerators', 577
  fields, 575
  File Access, \indexit{93}
  `FileDescriptorOfStream', 98
  `Filename', 92
  Filename, \indexit{92}
  File Operations, \indexit{94}
  File Streams, \indexit{103}
  `Filtered', 201
  Filters, \indexit{117}
  Filters Controlling the Arithmetic Behaviour of Lists, \indexit{184}
  Finding Positions in Lists, \indexit{190}
  Finding Submodules, \indexit{695}
  `FindSl2', 650
  Finish Installation and Cleanup, \indexit{831}
  Finite Field Elements, \indexit{581}
  Finitely Presented Lie Algebras, \indexit{650}
  Finitely presented monoids, \indexit{549}
  finiteness test, for a list or collection, 270
  Finite Perfect Groups, \indexit{520}
  `First', 202
  `FittingSubgroup', 361
  `Flat', 198
  flush character, 250
  For, \indexit{53}
  `ForAll', 203
  `ForAny', 203
  `for' loop, 53
  `FpElmComparisonMethod', 462
  `FpGroupPresentation', 480
  `FpGrpMonSmgOfFpGrpMonSmgElement', 547
  `FpLieAlgebraByCartanMatrix', 651
  frame, 786, 787
  `FrattiniSubgroup', 361
    \sub for groups with pcgs, 448
  `FreeAlgebra', 613
  `FreeAlgebraWithOne', 613
  `FreeAssociativeAlgebra', 613
  `FreeAssociativeAlgebraWithOne', 613
  `FreeGeneratorsOfFpGroup', 462
  `FreeGeneratorsOfFpSemigroup', 548
  `FreeGeneratorsOfWholeGroup', 462
  `FreeGroup', 329
  `FreeGroupOfFpGroup', 462
  Free Groups, Monoids and Semigroups, \indexit{329}
  `FreeLeftModule', 573
  `FreeLieAlgebra', 639
  `FreeMagma', 326
  `FreeMagmaRing', 661
  Free Magma Rings, \indexit{661}
  Free Magmas, \indexit{326}
  `FreeMagmaWithOne', 326
  Free Modules, \indexit{573}
  `FreeMonoid', 544
    \sub with example, 329
  `FreeMonoidOfRewritingSystem', 551
  `FreeProduct', 507
  Free Products, \indexit{507}
  `FreeSemigroup', 329
    \sub with examples, 537
  `FreeSemigroupOfFpSemigroup', 548
  `FreeSemigroupOfRewritingSystem', 551
  Frobenius automorphism, 586
  `FrobeniusAutomorphism', 586
  FrobeniusAutomorphism, \indexit{586}
  `FrobeniusCharacterValue', 796
  `FullMatrixAlgebra', 616
  `FullMatrixAlgebraCentralizer', 624
  `FullMatrixLieAlgebra', 639
  `FullMatrixModule', 574
  `FullMatrixSpace', 605
  `FullRowModule', 574
  `FullRowSpace', 605
  `FullTransformationSemigroup', 538
  Function, \indexit{55}
  `function', 55
  `FunctionAction', 406
  function call, 46
    \sub with arguments, 46
    \sub with options, 47
  Function Calls, \indexit{46}
  `FunctionOperation', 846
  functions, 61, 301
    \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{218}
  Functions for GAP Packages, \indexit{843}
  Functions that do nothing, \indexit{63}
  Function that Modify Boolean Lists, \indexit{211}
  Function Types, \indexit{63}
  `FusionCharTableTom', 718
  `FusionConjugacyClasses', 803
  `FusionConjugacyClassesOp', 803
  fusions, 802
  `FusionsAllowedByRestrictions', 818
  `FusionsTom', 707
\letter G
  $G$-sets, 394, 406
  $g_N$, 161
  `gac', 35
  Galois Action, \indexit{577}
  Galois Conjugacy of Cyclotomics, \indexit{164}
  `GaloisCyc', 164
    \sub for class functions, 770
  `GaloisField', 585
  `GaloisGroup', of field, 578
    \sub of rational class of a group, 359
  Galois Groups of Abelian Number Fields, \indexit{594}
  `GaloisMat', 165
  `GaloisStabilizer', 591
  `GaloisType', 676
  `gap.rc', 32, 33
  GAP3, 34
  `Gap3CatalogueIdGroup', 518
  GAP for Macintosh OS X, \indexit{837}
  GAP for MacOS, \indexit{838}
  `GAPInfo', 847
  `GAPInfo.RootPaths', 29
  `GapInputPcGroup', 455
  `GapInputSCTable', 614
  `GAPKB_REW', 550
  GAP Root Directory, \indexit{90}
  `GasmanLimits', 87
  `GasmanMessageStatus', 87
  `GasmanStatistics', 87
  Gaussian algorithm, 228
  `GaussianIntegers', 595
  `GaussianRationals', 590
  Gaussians, \indexit{595}
  `Gcd', 568
  Gcd and Lcm, \indexit{568}
  `Gcdex', 130
  `GcdInt', 129
  `GcdOp', 568
  `GcdRepresentation', 568
  `GcdRepresentationOp', 569
  General Binary Relations, \indexit{312}
  `GeneralisedEigenspaces', 229
  `GeneralisedEigenvalues', 229
  generalized characters, 764
  `GeneralizedEigenspaces', 229
  `GeneralizedEigenvalues', 229
  `GeneralLinearGroup', 511
  `GeneralMappingByElements', 302
  General Mappings, \indexit{310}
  `GeneralMappingsFamily', 311
  `GeneralOrthogonalGroup', 512
  `GeneralUnitaryGroup', 511
  Generating Fields, \indexit{575}
  Generating modules, \indexit{571}
  Generating Rings, \indexit{559}
  generator, of the prime residue group, 140
  `GeneratorsOfAdditiveGroup', 557
  `GeneratorsOfAdditiveMagma', 557
  `GeneratorsOfAdditiveMagmaWithZero', 557
  `GeneratorsOfAlgebra', 620
  `GeneratorsOfAlgebraModule', 631
  `GeneratorsOfAlgebraWithOne', 620
  `GeneratorsOfDivisionRing', 576
  `GeneratorsOfDomain', 290
  `Generators\-Of\-Equivalence\-Relation\-Partition', 315
  `GeneratorsOfField', 576
  `GeneratorsOfGroup', 348
  `GeneratorsOfIdeal', 562
  `GeneratorsOfLeftIdeal', 563
  `GeneratorsOfLeftModule', 571
  `GeneratorsOfLeftOperatorAdditiveGroup', 571
  `GeneratorsOfLeftVectorSpace', 597
  `GeneratorsOfMagma', 320
  `GeneratorsOfMagmaWithInverses', 320
  `GeneratorsOfMagmaWithOne', 320
  `GeneratorsOfMonoid', 543
  `GeneratorsOfNearAdditiveGroup', 557
  `GeneratorsOfNearAdditiveMagma', 557
  `GeneratorsOfNearAdditiveMagmaWithZero', 557
  `GeneratorsOfPresentation', 479
  `GeneratorsOfRightIdeal', 563
  `GeneratorsOfRightModule', 572
  `GeneratorsOfRightOperatorAdditiveGroup', 572
  `GeneratorsOfRing', 560
  `GeneratorsOfRingWithOne', 564
  `GeneratorsOfRws', 343
  `GeneratorsOfSemigroup', 537
  `GeneratorsOf<Struct>', 286
  `GeneratorsOfTwoSidedIdeal', 562
  `GeneratorsOfVectorSpace', 597
  `GeneratorsPrimeResidues', 139
  `GeneratorsSmallest', 377
  `GeneratorsSubgroupsTom', 716
  `GeneratorSyllable', 334
  Generic Construction of Tables of Marks, \indexit{720}
  `GetFusionMap', 804
  Get the Archives, \indexit{828}
  getting help, 22
  `GF', 585
  `GL', 511
  GL and SL, \indexit{428}
  Global Memory Information, \indexit{87}
  `GlobalMersenneTwister', 136
  `GlobalRandomSource', 136
  `GModuleByMats', 694
  `GO', 512
  `GQuotients', 391
  `Grading', 625
  Green's Relations, \indexit{539}
  `GreensDClasses', 541
  `GreensDClassOfElement', 540
  `GreensDRelation', 540
  `GreensHClasses', 541
  `GreensHClassOfElement', 540
  `GreensHRelation', 540
  `GreensJClasses', 541
  `GreensJClassOfElement', 540
  `GreensJRelation', 540
  `GreensLClasses', 541
  `GreensLClassOfElement', 540
  `GreensLRelation', 540
  `GreensRClasses', 541
  `GreensRClassOfElement', 540
  `GreensRRelation', 540
  Groebner Bases, \indexit{683}
  `GroebnerBasis', 683
  `GroebnerBasisNC', 683
  `Group', 347
  group actions, 394, 395
    \sub operations syntax, 394
  Group Actions - Name Changes, \indexit{846}
  group algebra, 660
  Group Automorphisms, \indexit{387}
  `GroupByRws', 453
  `GroupByRwsNC', 453
  group characters, 764
  Group Elements, \indexit{347}
  `GroupGeneralMappingByImages', 383
  `GroupHClassOfGreensDClass', 541
  `GroupHomomorphismByFunction', 383
  `GroupHomomorphismByImages', 382
  `GroupHomomorphismByImagesNC', 382
  `GroupOfPcgs', 435
  group operations, 395, 846
  Group Properties, \indexit{364}
  `GroupRing', 661
  group ring, 660
  Groups of Automorphisms, \indexit{389}
  `GroupStabChain', 422
  `GroupWithGenerators', 348
  `GU', 511
\letter H
  $h_N$, 161
  `HallSubgroup', 362
  `HallSystem', 363
    \sub for groups with pcgs, 448
  Handling of Streams in the Background, \indexit{106}
  `HasAbelianFactorGroup', 370
  `HasElementaryAbelianFactorGroup', 370
  `HasIndeterminateName', 667
  `HasParent', 288
  `HasseDiagramBinaryRelation', 314
  `HeadPcElementByNumber', 437
  `HenselBound', 676
  hermite normal form, 847
  `HermiteNormalFormIntegerMat', 241
  `HermiteNormalFormIntegerMatTransform', 241
  `HeuristicCancelPolynomials', 688
  `HexStringInt', 253
  `HighestWeightModule', 657
  History of Character Theory Stuff in GAP, \indexit{723}
  `HMSMSec', 258
  `Hom', 608
  `HomeEnumerator', 406
  Homomorphism for very large groups, \indexit{386}
  `HomomorphismQuotientSemigroup', 539
  homomorphisms, find all, 391
  homomorphisms, Frobenius, field, 586
  Homomorphisms of Algebras, \indexit{626}
  `HomomorphismTransformationSemigroup', 538
  How to Implement New Kinds of Vector Spaces, \indexit{610}
  `HumanReadableDefinition', 714
\letter I
  $i_N$, 162
  `Ideal', 561
  `IdealByGenerators', 562
  `IdealNC', 562
  Ideals, \indexit{618}
  Ideals in Rings, \indexit{561}
  Ideals of semigroups, \indexit{538}
  `Idempotents', 321
  `IdempotentsTom', 707
  `IdempotentsTomInfo', 707
  Identical Lists, \indexit{179}
  Identical Objects, \indexit{111}
  Identical Records, \indexit{261}
  `IdentificationOfConjugacyClasses', 729
  `Identifier', for character tables, 735
    \sub for tables of marks, 708
  Identifiers, \indexit{42}
  `Identity', 290
  `IdentityBinaryRelation', 312
  `IdentityFromSCTable', 615
  `IdentityMapping', 303
  `IdentityMat', 226
  `IdentityTransformation', 552
  `IdFunc', 63
  `IdGap3SolvableGroup', 518
  `IdGroup', 518
  `IdSmallGroup', 518
  `IdsOfAllSmallGroups', 518
  If, \indexit{51}
  `if' statement, 51
  If Things Go Wrong, \indexit{833}
  `Image', 305
    \sub for Frobenius automorphisms, 586
  image, vector under matrix, 223
  `ImageElm', 305
  `ImageListOfTransformation', 553
  `Images', 305
  `ImagesElm', 304
  `ImageSetOfTransformation', 553
  `ImagesRepresentative', 304
  `ImagesSet', 304
  `ImagesSmallestGenerators', 386
  `ImagesSource', 304
  Images under Mappings, \indexit{304}
  `ImfInvariants', 531
  `ImfMatrixGroup', 532
  `ImfNumberQClasses', 529
  `ImfNumberQQClasses', 529
  `ImfNumberZClasses', 529
  `Immutable', 113
  `ImmutableBasis', 604
  `ImmutableMatrix', 235
  `in', for collections, 274
    \sub for lists, 182
    \sub for strictly sorted lists, 195
    \sub operation for, 274
  `IndependentGeneratorsOfAbelianGroup', 377
  `Indeterminate', 666
  `IndeterminateName', 667
  `Indeterminateness', 812
  `IndeterminateNumberOfLaurentPolynomial', 677
  `Indeterminate\-Number\-Of\-Univariate\-Rational\-Function', 667
  `Indeterminate\-Of\-Univariate\-Rational\-Function', 667
  Indeterminates, \indexit{666}
  `IndeterminatesOfPolynomialRing', 678
  `Index', 349
  `IndexInWholeGroup', 349
  `IndexNC', 349
  Index numbers of primitive groups, \indexit{526}
  `Indicator', 743
  `IndicatorOp', 743
  `IndicesCentralNormalSteps', 442
  `IndicesChiefNormalSteps', 443
  `IndicesEANormalSteps', 442
  `IndicesInvolutaryGenerators', 467
  `IndicesNormalSteps', 444
  `IndicesOfAdjointBasis', 621
  `IndicesPCentralNormalStepsPGroup', 443
  `IndicesStabChain', 422
  `Indirected', 808
  Induced Actions, \indexit{696}
  `InducedAutomorphism', 390
  `InducedClassFunction', 778
  `InducedClassFunctions', 778
  `InducedCyclic', 779
  `InducedPcgs', 438
  `InducedPcgsByGenerators', 438
  `InducedPcgsByGeneratorsNC', 438
  `InducedPcgsByPcSequence', 438
  `InducedPcgsByPcSequenceAndGenerators', 439
  `InducedPcgsByPcSequenceNC', 438
  `InducedPcgsWrtFamilyPcgs', 451
  `InducedPcgsWrtSpecialPcgs', 446
  `Inequalities', 795
  inequality, of records, 262
  inequality test, 47
  `InertiaSubgroup', 776
  Infinity, \indexit{160}
  `infinity', 160
  inflated class functions, 777
  `Info', 80
  `InfoAlgebra', 612
  `InfoAttributes', 123
  `InfoBckt', 424
  `InfoCharacterTable', 728
  `InfoCoh', 379
  `InfoComplement', 360
  `InfoCoset', 357
  `InfoFpGroup', 461
  Info Functions, \indexit{80}
  `InfoGroebner', 684
  `InfoGroup', 348
  `InfoLattice', 374
  `InfoLevel', 80
  `InfoMatrix', 221
  `InfoMonomial', 820
  `InfoNumtheor', 138
  `InfoOptions', 89
  `InfoPcSubgroup', 377
  Information about a function, \indexit{61}
  Information about the version used, \indexit{84}
  `InfoText', 736
  `InfoTom', 705
  `InfoWarning', 81
  `Init', 136
  `InitFusion', 817
  `InitPowerMap', 815
  `InjectionZeroMagma', 319
  `InnerAutomorphism', 388
  `InnerAutomorphismNC', 388
  `InnerAutomorphismsAutomorphismGroup', 389
  inner product, of group characters, 774
  Input-Output Streams, \indexit{105}
  `InputLogTo', 95
    \sub for streams, 102
    \sub stop logging input, 95
  `InputOutputLocalProcess', 105
  `InputTextFile', 103
  `InputTextNone', 106
  `InputTextString', 104
  `InputTextUser', 104
  `InsertTrivialStabilizer', 423
  `InstallAtExit', 73
  installation, 827
  Installation of GAP for MacOS, \indexit{838}
  Installation Overview, \indexit{827}
  `InstallCharReadHookFunc', 106
  `InstalledPackageVersion', 844
  `InstallFactorMaintenance', 296
  `InstallHandlingByNiceBasis', 610
  Installing a GAP Package, \indexit{842}
  `InstallIsomorphismMaintenance', 296
  `InstallSubsetMaintenance', 296
  `Int', 127
    \sub for cyclotomics, 158
    \sub for strings, 256
  `INT_CHAR', 255
  integer part of a quotient, 129
  `Integers', 126
  Integral Bases of Abelian Number Fields, \indexit{592}
  `IntegralizedMat', 244
  `IntegratedStraightLineProgram', 339
  `IntermediateGroup', 369
  `IntermediateResultOfSLP', 340
  `IntermediateResultOfSLPWithoutOverwrite', 340
  `Intermediate\-Results\-Of\-SLPWithout\-Overwrite', 340
  `IntermediateSubgroups', 369
  Internally Represented Cyclotomics, \indexit{166}
  Internally Represented Strings, \indexit{251}
  `InterpolatedPolynomial', 570
  `IntersectBlist', 211
  `Intersection', 272
    \sub for groups with pcgs, 448
  intersection, of collections, 272
    \sub of sets, 197
  `Intersection2', 272
  `IntersectionBlist', 210
  `IntersectionsTom', 712
  `IntersectSet', 197
  `IntFFE', 584
  `IntFFESymm', 584
  `IntHexString', 256
  `IntScalarProducts', 812, 813
  `IntVecFFE', 584
  `InvariantBilinearForm', 429
  `InvariantElementaryAbelianSeries', 368
  Invariant Forms, \indexit{429}, \indexit{697}
  `InvariantLattice', 431
  `InvariantQuadraticForm', 429
  `InvariantSesquilinearForm', 429
  `Invariant\-Subgroups\-Elementary\-Abelian\-Group', 375
  `Inverse', 292
  inverse, group homomorphism, 384
    \sub matrix, 223
    \sub of class function, 769
  `InverseAttr', 292
  `InverseClasses', 736
  `InverseGeneralMapping', 302
  `InverseImmutable', 292
  `InverseMap', 808
  `InverseMatMod', 237
  `InverseMutable', 292
  `InverseOp', 292
  `InverseRepresentative', 422
  `InverseSameMutability', 292
  `InverseSM', 292
  Invoking the Help, \indexit{22}
  `Irr', 731
  irrationalities, 157
  `IrrBaumClausen', 748
  `IrrConlon', 748
  `IrrDixonSchneider', 748
  Irreducibility Tests, \indexit{695}
  irreducible character, 773
  irreducible characters, computation, 751
  `IrreducibleDifferences', 780
  Irreducible Maximal Finite Integral Matrix Groups, \indexit{528}
  `IrreducibleModules', 750
    \sub for groups with pcgs, 448
  `IrreducibleRepresentations', 749
  `IrreducibleRepresentationsDixon', 750
  `IrreducibleSolvableGroup', 527
  `IrreducibleSolvableGroupMS', 527
  Irreducible Solvable Matrix Groups, \indexit{527}
  `Is16BitsFamily', 335
  `Is32BitsFamily', 335
  `Is8BitsFamily', 335
  `IsAbelian', 321
    \sub for character tables, 733
  `IsAbelianNumberField', 591
  `IsAbelianNumberFieldPolynomialRing', 679
  `IsAbelianTom', 709
  `IsAdditiveElement', 297
  `IsAdditiveElementWithInverse', 297
  `IsAdditiveElementWithZero', 297
  `IsAdditiveGroup', 556
  `IsAdditiveGroupGeneralMapping', 309
  `IsAdditiveGroupHomomorphism', 309
  `IsAdditivelyCommutative', 557
  `IsAdditivelyCommutativeElement', 299
  `IsAdditivelyCommutativeElementCollColl', 299
  `Is\-Additively\-Commutative\-Element\-Collection', 299
  `IsAdditivelyCommutativeElementFamily', 299
  `IsAdditiveMagma', 555
  `IsAdditiveMagmaWithInverses', 556
  `IsAdditiveMagmaWithZero', 555
  `IsAlgebra', 619
  `IsAlgebraGeneralMapping', 310
  `IsAlgebraHomomorphism', 310
  `IsAlgebraicElement', 690
  `IsAlgebraicExtension', 689
  `IsAlgebraModuleElement', 631
  `IsAlgebraModuleElementCollection', 631
  `IsAlgebraModuleElementFamily', 631
  `IsAlgebraWithOne', 619
  `IsAlgebraWithOneGeneralMapping', 310
  `IsAlgebraWithOneHomomorphism', 310
  `IsAlphaChar', 252
  `IsAlternatingGroup', 415
  `IsAnticommutative', 565
  `IsAntisymmetricBinaryRelation', 313
  `IsAssociated', 566
  `IsAssociative', 321
  `IsAssociativeElement', 299
  `IsAssociativeElementCollColl', 299
  `IsAssociativeElementCollection', 299
  `IsAssocWord', 328
  `IsAssocWordWithInverse', 328
  `IsAssocWordWithOne', 328
  `IsAutomorphismGroup', 389
  `IsBasicWreathLessThanOrEqual', 331
  `IsBasicWreathProductOrdering', 283
  `IsBasis', 599
  `IsBasisByNiceBasis', 610
  `IsBasisOfAlgebraModuleElementSpace', 632
  `IsBergerCondition', 821
  `IsBijective', 304
  `IsBinaryRelation', 312
    \sub same as `IsEndoGeneralMapping', 312
  `IsBLetterAssocWordRep', 335
  `IsBLetterWordsFamily', 335
  `IsBlist', 209
  `IsBlockMatrixRep', 238
  `IsBool', 169
  `IsBound', for lists, 178
  IsBound and Unbind for Lists, \indexit{178}
  IsBound and Unbind for Records, \indexit{263}
  `IsBoundGlobal', 45
  `IsBrauerTable', 727
  `IsBravaisGroup', 431
  `IsBuiltFromAdditiveMagmaWithInverses', 344
  `IsBuiltFromGroup', 344
  `IsBuiltFromMagma', 344
  `IsBuiltFromMagmaWithInverses', 344
  `IsBuiltFromMagmaWithOne', 344
  `IsBuiltFromSemigroup', 344
  `IsCanonicalBasis', 602
  `IsCanonicalBasisFullMatrixModule', 606
  `IsCanonicalBasisFullRowModule', 606
  `IsCanonicalNiceMonomorphism', 387
  `IsCanonicalPcgs', 439
  `IsCentral', 321
  `IsCentralFactor', 380
  `IsChar', 248
  `IsCharacter', 773
  `IsCharacteristicSubgroup', 350
  `IsCharacterTable', 727
  `IsCharacterTableInProgress', 727
  `IsCharCollection', 248
  `IsCheapConwayPolynomial', 587
  `IsClassFunction', 764
  `IsClassFusionOfNormalSubgroup', 742
  `IsClosedStream', 97
  `IsCochain', 653
  `IsCochainCollection', 653
  `IsCollection', 265
  `IsCollectionFamily', 265
  `IsCommutative', 321
  `IsCommutativeElement', 299
  `IsCommutativeElementCollColl', 299
  `IsCommutativeElementCollection', 299
  `IsCompositionMappingRep', 302
  `IsConfluent', 342
    \sub for pc groups, 453
  `Is\-Conjugacy\-Class\-Subgroups\-By\-Stabilizer\-Rep', 371
  `IsConjugacyClassSubgroupsRep', 371
  `IsConjugate', 359
  `IsConjugatorAutomorphism', 388
  `IsConjugatorIsomorphism', 388
  `IsConstantRationalFunction', 671
  `IsConstantTimeAccessGeneralMapping', 310
  `IsConstantTimeAccessList', 173
  `IsContainedInSpan', 604
  `IsCopyable', 113
  `IsCyc', 158
  `IsCyclic', 364
    \sub for character tables, 733
  `IsCyclicTom', 709
  `IsCyclotomic', 158
  `IsCyclotomicField', 591
  `IsCyclotomicMatrixGroup', 430
  `IsDenseList', 172
  `IsDiagonalMat', 225
  `IsDigitChar', 252
  `IsDirectoryPath', 93
  `IsDistributive', 565
  `IsDivisionRing', 575
  `IsDomain', 289
  `IsDoneIterator', 276
  `IsDoubleCoset', 357
  `IsDuplicateFree', 193
  `IsDuplicateFreeList', 193
  `IsDxLargeGroup', 752
  `IsElementaryAbelian', 364
    \sub for character tables, 733
  `IsElementOfFpMonoid', 547
  `IsElementOfFpSemigroup', 547
  `IsElementOfFreeMagmaRing', 662
  `IsElementOfFreeMagmaRingCollection', 662
  `IsElementOfFreeMagmaRingFamily', 662
  `IsElementOfMagmaRingModuloRelations', 663
  `Is\-Element\-Of\-Magma\-Ring\-Modulo\-Relations\-Collection', 663
  `Is\-Element\-Of\-Magma\-Ring\-Modulo\-Relations\-Family', 663
  `Is\-Element\-Of\-Magma\-Ring\-Modulo\-Span\-Of\-Zero\-Family', 664
  `IsEmpty', 270
  `IsEmptyString', 251
  `IsEndOfStream', 100
  `IsEndoGeneralMapping', 310
    \sub same as `IsBinaryRelation', 312
  `IsEqualSet', 196
  `IsEquivalenceClass', 316
  `IsEquivalenceRelation', 313
  `IsEuclideanRing', 567
  `IsEvenInt', 127
  `IsExecutableFile', 93
  `IsExistingFile', 93
  `IsExtAElement', 297
  `IsExternalOrbit', 407
  `IsExternalSet', 406
  `IsExternalSubset', 407
  `IsExtLElement', 297
  `IsExtRElement', 297
  `IsFamilyPcgs', 451
  `IsFFE', 581
  `IsFFECollColl', 581
  `IsFFECollection', 581
  `IsField', 575
  `IsFieldControlledByGaloisGroup', 578
  `IsFieldHomomorphism', 310
  `IsFinite', 270
    \sub for character tables, 733
  `IsFiniteDimensional', 573
    \sub for matrix algebras, 620
  `IsFiniteFieldPolynomialRing', 679
  `IsFinitelyGeneratedGroup', 365
  `IsFiniteOrderElement', 299
  `IsFiniteOrderElementCollColl', 299
  `IsFiniteOrderElementCollection', 299
  `IsFiniteOrdersPcgs', 435
  `IsFixedStabilizer', 424
  `IsFLMLOR', 619
  `IsFLMLORWithOne', 619
  `IsFpGroup', 461
  `IsFpMonoid', 547
  `IsFpSemigroup', 547
  `IsFreeGroup', 329
  `IsFreeLeftModule', 573
  `IsFreeMagmaRing', 661
  `IsFreeMagmaRingWithOne', 661
  `IsFromFpGroupGeneralMappingByImages', 393
  `IsFromFpGroupHomomorphismByImages', 393
  `Is\-From\-Fp\-Group\-Std\-Gens\-General\-Mapping\-By\-Images', 393
  `Is\-From\-Fp\-Group\-Std\-Gens\-Homomorphism\-By\-Images', 393
  `IsFullHomModule', 609
  `IsFullMatrixModule', 574
  `IsFullRowModule', 574
  `Is\-Full\-Subgroup\-GLor\-SLRespecting\-Bilinear\-Form', 429
  `Is\-Full\-Subgroup\-GLor\-SLRespecting\-Quadratic\-Form', 430
  `Is\-Full\-Subgroup\-GLor\-SLRespecting\-Sesquilinear\-Form', 429
  `IsFullTransformationSemigroup', 538
  `IsFunction', 63
  `IsGAPRandomSource', 136
  `IsGaussianIntegers', 595
  `IsGaussianRationals', 590
  `IsGaussianSpace', 604
  `IsGaussInt', 160
  `IsGaussRat', 160
  `IsGeneralizedDomain', 289
  `IsGeneralizedRowVector', 184
  `IsGeneralLinearGroup', 428
  `IsGeneralMapping', 310
  `IsGeneralMappingFamily', 311
  `IsGeneratorsOf<Struct>', 286
  `IsGL', 428
  `IsGlobalRandomSource', 136
  `IsGreensClass', 540
  `IsGreensDClass', 540
  `IsGreensDRelation', 540
  `IsGreensHClass', 540
  `IsGreensHRelation', 540
  `IsGreensJClass', 540
  `IsGreensJRelation', 540
  `IsGreensLClass', 540
  `IsGreensLessThanOrEqual', 540
  `IsGreensLRelation', 540
  `IsGreensRClass', 540
  `IsGreensRelation', 540
  `IsGreensRRelation', 540
  `IsGroup', 348
  `IsGroupGeneralMapping', 308
  `Is\-Group\-General\-Mapping\-By\-As\-Group\-General\-Mapping\-By\-Images', 393
  `IsGroupGeneralMappingByImages', 393
  `IsGroupGeneralMappingByPcgs', 393
  `IsGroupHClass', 541
  `IsGroupHomomorphism', 308
  `IsGroupOfAutomorphisms', 389
  `IsGroupRing', 661
  `IsHandledByNiceBasis', 574
    \sub for vector spaces, 610
  `IsHandledByNiceMonomorphism', 387
  `IsHasseDiagram', 313
  `IsHomogeneousList', 173
  `IsIdempotent', 292
  `IsIdenticalObj', 111
  `IsIncomparableUnder', 279
  `IsInducedFromNormalSubgroup', 823
  `IsInducedPcgs', 438
  `IsInducedPcgsWrtSpecialPcgs', 446
  `IsInfBitsFamily', 335
  `IsInfinity', 160
  `IsInjective', 304
  `IsInnerAutomorphism', 388
  `IsInputOutputStream', 105
  `IsInputStream', 97
  `IsInputTextNone', 97
  `IsInputTextStream', 97
  `IsInt', 127
  `IsIntegerMatrixGroup', 431
  `IsIntegers', 126
  `IsIntegralBasis', 602
  `IsIntegralCyclotomic', 158
  `IsIntegralRing', 564
  `IsInternallyConsistent', 115
    \sub for character tables, 742
    \sub for tables of marks, 710
  `IsIrreducibleCharacter', 773
  `IsIrreducibleRingElement', 566
  `IsIterator', 276
  `IsJacobianElement', 299
  `IsJacobianElementCollColl', 299
  `IsJacobianElementCollection', 299
  `IsJacobianRing', 565
  `IsLaurentPolynomial', 670
  `IsLaurentPolynomialDefaultRep', 686
  `IsLDistributive', 565
  `IsLeftAlgebraModuleElement', 631
  `IsLeftAlgebraModuleElementCollection', 631
  `IsLeftIdeal', 562
  `IsLeftIdealInParent', 562
  `IsLeftModule', 571
  `IsLeftModuleGeneralMapping', 309
  `IsLeftModuleHomomorphism', 309
  `IsLeftOperatorAdditiveGroup', 571
  `IsLeftSemigroupIdeal', 538
  `IsLeftVectorSpace', 596
  `IsLessThanOrEqualUnder', 279
  `IsLessThanUnder', 279
  `IsLetterAssocWordRep', 334
  `IsLetterWordsFamily', 334
  `IsLexicographicallyLess', 199
  `IsLexOrderedFFE', 582
  `IsLieAbelian', 642
  `IsLieAlgebra', 619
  `IsLieMatrix', 222
  `IsLieNilpotent', 642
  `IsLieObject', 637
  `IsLieObjectCollection', 637
  `IsLieSolvable', 642
  `IsLinearMapping', 309
  `IsLinearMappingsModule', 609
  `IsList', 172
  `IsListDefault', 184
  `IsListOrCollection', 266
  `IsLogOrderedFFE', 582
  `IsLowerAlphaChar', 252
  `IsLowerTriangularMat', 225
  `IsMagma', 317
  `IsMagmaHomomorphism', 307
  `IsMagmaRingModuloRelations', 663
  `IsMagmaRingModuloSpanOfZero', 664
  `IsMagmaWithInverses', 317
  `IsMagmaWithInversesIfNonzero', 317
  `IsMagmaWithOne', 317
  `IsMapping', 303
  `IsMatchingSublist', 193
  `IsMatrix', 221
  `IsMatrixGroup', 427
  `IsMatrixModule', 574
  `IsMatrixSpace', 604
  `IsMersenneTwister', 136
  `IsMinimalNonmonomial', 826
  `IsModuloPcgs', 440
  `IsMonoid', 543
  `IsMonomial', for characters, 823
    \sub for character tables, 733
    \sub for groups, 823
    \sub for positive integers, 824
  `IsMonomialGroup', 364
  `IsMonomialMatrix', 225
  `IsMonomialNumber', 824
  `IsMonomialOrdering', 680
  `IsMultiplicativeElement', 297
  `IsMultiplicativeElementWithInverse', 298
  `IsMultiplicativeElementWithOne', 298
  `IsMultiplicativeElementWithZero', 298
  `IsMultiplicativeGeneralizedRowVector', 184
  `IsMultiplicativeZero', 321
  `IsMutable', 113
  `IsMutableBasis', 603
  `IsNaturalAlternatingGroup', 414
  `IsNaturalGL', 429
  `IsNaturalGLnZ', 431
  `IsNaturalSL', 429
  `IsNaturalSLnZ', 431
  `IsNaturalSymmetricGroup', 414
  `IsNearAdditiveElement', 297
  `IsNearAdditiveElementWithInverse', 297
  `IsNearAdditiveElementWithZero', 297
  `IsNearAdditiveGroup', 555
  `IsNearAdditiveMagma', 555
  `IsNearAdditiveMagmaWithInverses', 555
  `IsNearAdditiveMagmaWithZero', 555
  `IsNearlyCharacterTable', 727
  `IsNearRingElement', 298
  `IsNearRingElementWithInverse', 298
  `IsNearRingElementWithOne', 298
  `IsNegRat', 146
  `IsNilpotent', for character tables, 733
    \sub for groups with pcgs, 448
  `IsNilpotentElement', 649
  `IsNilpotentGroup', 364
  `IsNilpotentTom', 709
  `IsNonassocWord', 324
  `IsNonassocWordCollection', 324
  `IsNonassocWordWithOne', 324
  `IsNonassocWordWithOneCollection', 324
  `IsNonnegativeIntegers', 126
  `IsNonSPGeneralMapping', 311
  `IsNonTrivial', 270
  `IsNormal', 349
  `IsNormalBasis', 602
  `IsNotIdenticalObj', 112
  `IsNumberField', 591
  `IsObject', 110
  `IsOddInt', 127
  isomorphic, pc group, 454, 455
  `IsomorphicSubgroups', 391
  `IsomorphismFpAlgebra', 628
  `IsomorphismFpGroup', 470
    \sub for subgroups of fp groups, 472
  `IsomorphismFpGroupByGenerators', 470
  `IsomorphismFpGroupByGeneratorsNC', 470
  `IsomorphismFpGroupByPcgs', 452
  `IsomorphismFpSemigroup', 548
  `IsomorphismGroups', 391
  `IsomorphismMatrixAlgebra', 628
  `IsomorphismPcGroup', 455
  `IsomorphismPermGroup', 414
    \sub for Imf matrix groups, 534
  `IsomorphismPermGroupImfGroup', 535
  `IsomorphismReesMatrixSemigroup', 542
  `IsomorphismRefinedPcGroup', 454
  `Isomorphism<Rep><Struct>', 287
  isomorphisms, find all, 391
  `IsomorphismSCAlgebra', 629
  `IsomorphismSimplifiedFpGroup', 473
  `IsomorphismSpecialPcGroup', 455
  `IsomorphismTransformationSemigroup', 538
  `IsomorphismTypeInfoFiniteSimpleGroup', 365
  `IsOne', 292
  `IsOperation', 63
  `IsOrdering', 278
  `IsOrderingOnFamilyOfAssocWords', 280
  `IsOrdinaryMatrix', 221
  `IsOrdinaryTable', 727
  `IsOutputStream', 98
  `IsOutputTextNone', 98
  `IsOutputTextStream', 98
  `IsPadicExtensionNumber', 693
  `IsPadicExtensionNumberFamily', 693
  `IsParentPcgsFamilyPcgs', 451
  `IsPartialOrderBinaryRelation', 313
  `IsPcGroup', 452
  `IsPcGroupGeneralMappingByImages', 393
  `IsPcGroupHomomorphismByImages', 393
  `IsPcgs', 434
  `IsPcgsCentralSeries', 442
  `IsPcgsChiefSeries', 443
  `IsPcgsElementaryAbelianSeries', 442
  `IsPcgsPCentralSeriesPGroup', 443
  `IsPerfect', for character tables, 733
  `IsPerfectGroup', 364
  `IsPerfectTom', 709
  `IsPerm', 409
  `IsPermCollColl', 409
  `IsPermCollection', 409
  `IsPermGroup', 413
  `IsPermGroupGeneralMappingByImages', 393
  `IsPermGroupHomomorphismByImages', 393
  `IsPGroup', 365
  `IsPNilpotent', 366
  `IsPolycyclicGroup', 364
  `IsPolynomial', 670
  `IsPolynomialDefaultRep', 686
  `IsPolynomialFunction', 669
  `IsPolynomialFunctionsFamily', 684
  `IsPolynomialRing', 679
  `IsPosInt', 127
  `IsPositiveIntegers', 126
  `IsPosRat', 146
  `Is\-Preimages\-By\-As\-Group\-General\-Mapping\-By\-Images', 393
  `IsPreOrderBinaryRelation', 313
  `IsPrime', 566
  `IsPrimeField', 577
  `IsPrimeInt', 131
  `IsPrimeOrdersPcgs', 435
  `IsPrimePowerInt', 132
  `IsPrimitive', 405
  `IsPrimitiveCharacter', 822
  `IsPrimitivePolynomial', 671
  `IsPrimitiveRootMod', 140
  `IsProbablyPrimeInt', 131
  `IsPseudoCanonicalBasisFullHomModule', 609
  `IsPSolvable', 366
  `IsPSolvableCharacterTable', 742
  `IsPSolvableCharacterTableOp', 742
  `IsPurePadicNumber', 692
  `IsPurePadicNumberFamily', 692
  `IsQuasiPrimitive', 822
  `IsQuaternion', 620
  `IsQuaternionCollColl', 620
  `IsQuaternionCollection', 620
  `IsQuickPositionList', 208
  `IsQuotientSemigroup', 539
  `IsRandomSource', 136
  `IsRange', 207
  `IsRat', 145
  `IsRationalFunction', 669
  `IsRationalFunctionDefaultRep', 686
  `IsRationalFunctionsFamily', 684
  `IsRationalMatrixGroup', 430
  `IsRationals', 145
  `IsRationalsPolynomialRing', 679
  `IsRDistributive', 565
  `IsReadableFile', 93
  `IsReadOnlyGlobal', 44
  `IsRecord', 259
  `IsRecordCollColl', 259
  `IsRecordCollection', 259
  `IsReduced', 343
  `IsReductionOrdering', 280
  `IsReesCongruence', 539
  `IsReesCongruenceSemigroup', 538
  `IsReesMatrixSemigroup', 541
  `IsReesMatrixSemigroupElement', 542
  `IsReesZeroMatrixSemigroup', 541
  `IsReesZeroMatrixSemigroupElement', 542
  `IsReflexiveBinaryRelation', 312
  `IsRegular', 404
  `IsRegularDClass', 541
  `IsRegularSemigroup', 537
  `IsRegularSemigroupElement', 537
  `IsRelativelySM', 825
  `IsRestrictedLieAlgebra', 647
  `IsRewritingSystem', 342
  `IsRightAlgebraModuleElement', 631
  `IsRightAlgebraModuleElementCollection', 631
  `IsRightCoset', 355
  `IsRightIdeal', 562
  `IsRightIdealInParent', 562
  `IsRightModule', 572
  `IsRightOperatorAdditiveGroup', 571
  `IsRightSemigroupIdeal', 538
  `IsRing', 559
  `IsRingElement', 298
  `IsRingElementWithInverse', 298
  `IsRingElementWithOne', 298
  `IsRingGeneralMapping', 310
  `IsRingHomomorphism', 310
  `IsRingWithOne', 563
  `IsRingWithOneGeneralMapping', 310
  `IsRingWithOneHomomorphism', 310
  `IsRootSystem', 644
  `IsRootSystemFromLieAlgebra', 644
  `IsRowModule', 574
  `IsRowSpace', 604
  `IsRowVector', 213
  `IsScalar', 298
  `IsSemiEchelonized', 605
  `IsSemigroup', 536
  `IsSemigroupCongruence', 539
  `IsSemigroupIdeal', 538
  `IsSemiRegular', 404
  `IsSet', 193
  `IsShortLexLessThanOrEqual', 331
  `IsShortLexOrdering', 281
  `IsSimple', for character tables, 733
  `IsSimpleAlgebra', 620
  `IsSimpleGroup', 364
  `IsSimpleSemigroup', 537
  `IsSingleValued', 303
  `IsSL', 429
  `IsSolvable', for character tables, 733
  `IsSolvableGroup', 364
  `IsSolvableTom', 709
  `IsSortedList', 193
  `IsSpecialLinearGroup', 429
  `IsSpecialPcgs', 445
  `IsSPGeneralMapping', 311
  `IsSporadicSimple', for character tables, 733
  `IsSSortedList', 193
  `IsStandardGeneratorsOfGroup', 715
  `IsStraightLineProgElm', 340
  `IsStraightLineProgram', 336
  `IsStream', 97
  `IsString', 248
  `IsStringRep', 251
  `Is<Struct>', 287
  `IsSubgroup', 349
  `IsSubgroupFpGroup', 461
  `IsSubgroupOfWholeGroupByQuotientRep', 474
  `IsSubgroupSL', 429
  `IsSubmonoidFpMonoid', 546
  `IsSubnormal', 350
  `IsSubnormallyMonomial', 825
  `IsSubsemigroupFpSemigroup', 546
  `IsSubset', 272
  `IsSubsetBlist', 210
  `IsSubsetLocallyFiniteGroup', 365
  `IsSubsetSet', 196
  `IsSubspacesVectorSpace', 598
  `IsSub<struct>', 289
  `IsSupersolvable', for character tables, 733
    \sub for groups with pcgs, 448
  `IsSupersolvableGroup', 364
  `IsSurjective', 304
  `IsSyllableAssocWordRep', 335
  `IsSyllableWordsFamily', 335
  `IsSymmetricBinaryRelation', 313
  `IsSymmetricGroup', 415
  `IsTable', 173
  `IsTableOfMarks', 705
  `IsTableOfMarksWithGens', 716
  `IsToPcGroupGeneralMappingByImages', 393
  `IsToPcGroupHomomorphismByImages', 393
  `IsToPermGroupGeneralMappingByImages', 393
  `IsToPermGroupHomomorphismByImages', 393
  `IsTotal', 303
  `IsTotalOrdering', 279
  `IsTransformation', 552
  `IsTransformationCollection', 552
  `IsTransformationMonoid', 538
  `IsTransformationSemigroup', 538
  `IsTransitive', for characters, 776
    \sub for class functions, 776
    \sub for group actions, 404
  `IsTransitiveBinaryRelation', 313
  `IsTranslationInvariantOrdering', 280
  `IsTrivial', 270
  `IsTuple', 301
  `IsTwoSidedIdeal', 562
  `IsTwoSidedIdealInParent', 562
  `IsUEALatticeElement', 656
  `IsUEALatticeElementCollection', 656
  `IsUEALatticeElementFamily', 656
  `IsUniqueFactorizationRing', 564
  `IsUnit', 565
  `IsUnivariatePolynomial', 670
  `IsUnivariatePolynomialRing', 680
  `IsUnivariateRationalFunction', 670
  `IsUnknown', 167
  `IsUpperAlphaChar', 252
  `IsUpperTriangularMat', 225
  `IsValidIdentifier', 42
  `IsVector', 298
  `IsVectorSpace', 596
  `IsVirtualCharacter', 773
  `IsWeightLexOrdering', 282
  `IsWeightRepElement', 657
  `IsWeightRepElementCollection', 657
  `IsWeightRepElementFamily', 657
  `IsWellFoundedOrdering', 279
  `IsWeylGroup', 645
  `IsWholeFamily', 271
  `IsWLetterAssocWordRep', 335
  `IsWLetterWordsFamily', 335
  `IsWord', 323
  `IsWordCollection', 324
  `IsWordWithInverse', 323
  `IsWordWithOne', 323
  `IsWreathProductOrdering', 283
  `IsWritableFile', 93
  `IsZero', 292
  `IsZeroGroup', 538
  `IsZeroSimpleSemigroup', 537
  `IsZeroSquaredElement', 300
  `IsZeroSquaredElementCollColl', 300
  `IsZeroSquaredElementCollection', 300
  `IsZeroSquaredRing', 565
  `IsZmodnZObj', 135
  `IsZmodnZObjNonprime', 135
  `IsZmodpZObj', 135
  `IsZmodpZObjLarge', 135
  `IsZmodpZObjSmall', 135
  `Iterated', 204
  `Iterator', 275
  iterator, for low index subgroups, 469
  `IteratorByBasis', 601
  `IteratorByFunctions', 277
  `IteratorList', 277
  Iterators, \indexit{275}
  `IteratorSorted', 276
\letter J
  $j_N$, 162
  `Jacobi', 140
  `JenningsLieAlgebra', 648
  `JenningsSeries', 369
  `JoinEquivalenceRelations', 315
  `JoinStringsWithSeparator', 254
  `JordanDecomposition', 234
\letter K
  $k_N$, 162
  `KappaPerp', 649
  `KB_REW', 550
  `KernelOfAdditiveGeneralMapping', 309
  `KernelOfCharacter', 775
  `KernelOfMultiplicativeGeneralMapping', 308
  `KernelOfTransformation', 553
  Keywords, \indexit{41}
  `KillingMatrix', 649
  `KnownAttributesOfObject', 121
  Known Problems of the Configure Process, \indexit{834}
  `KnownPropertiesOfObject', 124
  `KnownTruePropertiesOfObject', 124
  `KnowsHowToDecompose', 381
  `KnuthBendixRewritingSystem', 551
  Krasner-Kaloujnine theorem, 506
  `KroneckerProduct', 227
  `KuKGenerators', 506
\letter L
  $l_N$, 162
  `Lambda', 138
  Language Overview, \indexit{39}
  larger or equal, 47
  larger test, 47
  `LargestElementGroup', 377
  `LargestElementStabChain', 422
  `LargestMovedPoint', 410
  `LargestUnknown', 167
  `last', 64
  `LastSystemError', 90
  `LaTeXStringDecompositionMatrix', 740
  lattice base reduction, 244, 245
  lattice basis reduction, for virtual characters, 780
  `LatticeByCyclicExtension', 374
  `LatticeGeneratorsInUEA', 656
  Lattice Reduction, \indexit{244}
  `LatticeSubgroups', 372
  `LatticeSubgroupsByTom', 703
  `LaurentPolynomialByCoefficients', 677
  `LaurentPolynomialByExtRep', 687
  `LaurentPolynomialByExtRepNC', 687
  Laurent Polynomials, \indexit{677}
  `LClassOfHClass', 540
  `Lcm', 569
  `LcmInt', 130
  `LcmOp', 569
  `LeadCoeffsIGS', 439
  `LeadingCoefficient', 672
  `LeadingCoefficientOfPolynomial', 681
  `LeadingExponentOfPcElement', 436
  `LeadingMonomial', 673
  `LeadingMonomialOfPolynomial', 680
  `LeadingTermOfPolynomial', 680
  Leaving GAP, \indexit{73}
  `LeftActingAlgebra', 632
  `LeftActingDomain', 572
  `LeftActingRingOfIdeal', 563
  `LeftAlgebraModule', 630
  `LeftAlgebraModuleByGenerators', 630
  left cosets, 355
  `LeftDerivations', 639
  `LeftIdeal', 561
  `LeftIdealByGenerators', 562
  `LeftIdealNC', 562
  `LeftModuleByGenerators', 572
  `LeftModuleByHomomorphismToMatAlg', 633
  `LeftModuleGeneralMappingByImages', 607
  `LeftModuleHomomorphismByImages', 607
  `LeftModuleHomomorphismByImagesNC', 607
  `LeftModuleHomomorphismByMatrix', 608
  `LeftQuotient', 294
    \sub for words, 332
  `LeftShiftRowVector', 217
  legacy, 846
  `Legendre', 141
  `Length', 194
    \sub of an associative word, 332
  length, of a word, 332
  `LengthsTom', 706
  `LenstraBase', 593
  `LessThanFunction', 279
  `LessThanOrEqualFunction', 279
  `LetterRepAssocWord', 335
  `LevelsOfGenerators', 283
  `LeviMalcevDecomposition', 625
    \sub for Lie algebras, 643
  Lexical Structure, \indexit{40}
  `LexicographicOrdering', 280
  `LGFirst', 446
  `LGLayers', 446
  `LGLength', 446
  `LGWeights', 445
  library tables, 724
  `LieAlgebra', 638
  `LieAlgebraByStructureConstants', 638
  `LieBracket', 294
  `LieCenter', 640
  `LieCentralizer', 640
  `LieCentre', 640
  `LieCoboundaryOperator', 653
  `LieDerivedSeries', 641
  `LieDerivedSubalgebra', 641
  `LieFamily', 638
  `LieLowerCentralSeries', 642
  `LieNilRadical', 641
  `LieNormalizer', 640
  `LieObject', 637
  Lie objects, \indexit{637}
  `LieSolvableRadical', 641
  `LieUpperCentralSeries', 642
  `LiftedInducedPcgs', 441
  `LiftedPcElement', 441
  `LinearAction', 447
  `LinearActionLayer', 447
  `LinearCharacters', 732
  `LinearCombination', 601
  `LinearCombinationPcgs', 436
  Linear equations over the integers and Integral Matrices, \indexit{239}
  `LinearIndependentColumns', 244
  Linear Mappings, \indexit{309}
  `LinearOperation', 447
  `LinearOperationLayer', 447
  Line Editing, \indexit{74}
  `LinesOfStraightLineProgram', 337
  `List', 201
  list and non-list, difference, 186
    \sub left quotient, 188
    \sub mod, 188
    \sub product, 187
    \sub quotient, 188
  List Assignment, \indexit{176}
  list assignment, operation, 174
  `ListBlist', 210
  list boundedness test, operation, 174
  List Categories, \indexit{172}
  list element, access, 174
    \sub assignment, 176
    \sub operation, 174
  List Elements, \indexit{174}
  list equal, comparison, 182
  `ListN', 204
  list of available books, 23
  `ListPerm', 412
  Lists and Collections, \indexit{266}
  list smaller, comparison, 183
  `ListStabChain', 422
  list unbind, operation, 174
  `ListWithIdenticalEntries', 189
  `ListX', 205
  `LLL', 780
  LLL algorithm, for Gram matrices, 245
    \sub for vectors, 244
    \sub for virtual characters, 780
  `LLLReducedBasis', 244
  `LLLReducedGramMat', 245
  `LoadDynamicModule', 35
  Loading a GAP Package, \indexit{842}
  loading a saved workspace, 37
  `LoadPackage', 842
  `local', 55
  logarithm, discrete, 140
    \sub of a root of unity, 160
  `LogFFE', 583
  logical, 169
  logical operations, 170
  `LogInt', 128
  `LogMod', 139
  `LogModShanks', 139
  `LogTo', 95
    \sub for streams, 102
    \sub stop logging, 95
  `LongestWeylWordPerm', 646
  loop, read eval print, 64
  loop, `for', 53
    \sub `repeat', 52
    \sub `while', 52
  loop over iterator, 54
  loop over object, 54
  loop over range, 53
  loops, leaving, 55
    \sub restarting, 55
  `LowercaseString', 253
  `LowerCentralSeriesOfGroup', 368
  Low Index Subgroups, \indexit{469}
  `LowIndexSubgroupsFpGroup', 469
  `LowIndexSubgroupsFpGroupIterator', 469
  Low Level Routines to Modify and Create Stabilizer Chains, \indexit{423}
  `Lucas', 155
\letter M
  $m_N$, 162
  Macintosh, 837, 838
  MacOS, 838
  `Magma', 318
  `MagmaByGenerators', 318
  `MagmaByMultiplicationTable', 319
  Magma Categories, \indexit{317}
  `MagmaElement', 319
  Magma Generation, \indexit{318}
  `MagmaHomomorphismByFunctionNC', 307
  Magma Homomorphisms, \indexit{307}
  `MagmaRingModuloSpanOfZero', 664
  Magma Rings modulo Relations, \indexit{663}
  Magma Rings modulo the Span of a Zero Element, \indexit{664}
  Magmas Defined by Multiplication Tables, \indexit{319}
  `MagmaWithInverses', 318
  `MagmaWithInversesByGenerators', 318
  `MagmaWithInversesByMultiplicationTable', 319
  `MagmaWithOne', 318
  `MagmaWithOneByGenerators', 318
  `MagmaWithOneByMultiplicationTable', 319
  Main Loop, \indexit{64}
  `MakeConfluent', 343
  `MakeImmutable', 113
  `MakeReadOnlyGlobal', 44
  `MakeReadWriteGlobal', 44
  Making transformation semigroups, \indexit{538}
  Manual Conventions, \indexit{20}
  map, parametrized, 807
  `MappedWord', 325
  `MappingByFunction', 302
  `MappingPermListList', 412
  Mappings that Respect Addition, \indexit{309}
  Mappings that Respect Multiplication, \indexit{308}
  Mappings which are Compatible with Algebraic Structures, \indexit{307}
  maps, 798
  `MarksTom', 706
  `MatAlgebra', 616
  `MatClassMultCoeffsCharTable', 744
  `MathieuGroup', 510
  `MatLieAlgebra', 639
  matrices, commutator, 224
  Matrices as Basis of a Row Space, \indexit{232}
  Matrices as Linear Mappings, \indexit{233}
  Matrices over Finite Fields, \indexit{235}
  Matrices Representing Linear Equations and the Gaussian Algorithm, \indexit{228}
  `MatrixAlgebra', 616
  `MatrixAutomorphisms', 760
  matrix automorphisms, 801
  `MatrixByBlockMatrix', 238
  Matrix Constructions, \indexit{226}
  Matrix Groups in Characteristic 0, \indexit{430}
  `MatrixLieAlgebra', 639
  `MatrixOfAction', 632
  matrix spaces, 604
  `MatScalarProducts', 774
  `MatTom', 708
  `MaximalAbelianQuotient', 370
  `MaximalBlocks', 405
  `MaximalNormalSubgroups', 372
  `MaximalSubgroupClassReps', 371
  `MaximalSubgroups', 371
    \sub for groups with pcgs, 448
  `MaximalSubgroupsLattice', 373
  `MaximalSubgroupsTom', 712
  `Maximum', 199
  `MaximumList', 200
  MeatAxe Modules, \indexit{694}
  `MeetEquivalenceRelations', 315
  `MeetMaps', 810
  Membership Test for Collections, \indexit{274}
  Membership Test for Lists, \indexit{182}
  `MinimalElementCosetStabChain', 422
  `MinimalGeneratingSet', 377
    \sub for groups with pcgs, 448
  `MinimalNonmonomialGroup', 826
  Minimal Nonmonomial Groups, \indexit{826}
  `MinimalNormalSubgroups', 372
  `MinimalPolynomial', 674
    \sub over a field, 578
    \sub over a ring, 674
  Minimal Polynomials, \indexit{674}
  `MinimalStabChain', 420
  `MinimalSupergroupsLattice', 373
  `MinimalSupergroupsTom', 713
  `MinimizedBombieriNorm', 676
  `Minimum', 200
  `MinimumList', 200
  `MinusCharacter', 816
  Miscellaneous, \indexit{144}
  Miscellaneous Name Changes or Removed Names, \indexit{847}
  mod, integers, 135
    \sub laurent polynomials, 668
    \sub lists, 188
    \sub rationals, 48
  `mod', 48
    \sub arithmetic operators, 48
    \sub for character tables, 731
    \sub residue class rings, 134
  modular inverse, 48
  modular remainder, 48
  modular roots, 142
  `ModuleByRestriction', 634
  Module Constructions, \indexit{694}
  Module Homomorphisms, \indexit{697}
  `ModuleOfExtension', 457
  Modules over Lie Algebras and Their Cohomology, \indexit{652}
  Modules over Semisimple Lie Algebras, \indexit{654}
  modulo, 48
    \sub arithmetic operators, 48
    \sub for pcgs, 440
    \sub residue class rings, 134
  `ModuloPcgs', 440
  `MoebiusMu', 143
  `MoebiusTom', 708
  Molien Series, \indexit{787}
  `MolienSeries', 787
  `MolienSeriesInfo', 788
  `MolienSeriesWithGivenDenominator', 789
  `Monoid', 543
  `MonoidByGenerators', 543
  `MonoidByMultiplicationTable', 544
  `MonoidOfRewritingSystem', 551
  `MonomialComparisonFunction', 681
  `MonomialExtGrlexLess', 683
  `MonomialExtrepComparisonFun', 681
  `MonomialGrevlexOrdering', 682
  `MonomialGrlexOrdering', 682
  `MonomialLexOrdering', 681
  Monomial Orderings, \indexit{680}
  `MonomialTotalDegreeLess', 847
  monomorphisms, find all, 391
  `MorClassLoop', 391
  More about Boolean Lists, \indexit{212}
  More About Global Variables, \indexit{44}
  More about Tables of Marks, \indexit{700}
  `MostFrequentGeneratorFpGroup', 467
  `MovedPoints', 411
  Moved Points of Permutations, \indexit{410}
  `MTX.BasesCompositionSeries', 696
  `MTX.BasesMaximalSubmodules', 696
  `MTX.BasesMinimalSubmodules', 695
  `MTX.BasesMinimalSupermodules', 696
  `MTX.BasesSubmodules', 695
  `MTX.BasisInOrbit', 697
  `MTX.BasisRadical', 696
  `MTX.BasisSocle', 696
  `MTX.CollectedFactors', 696
  `MTX.CompositionFactors', 696
  `MTX.DegreeSplittingField', 695
  `MTX.Dimension', 695
  `MTX.Distinguish', 697
  `MTX.Field', 695
  `MTX.Generators', 695
  `MTX.Homomorphism', 697
  `MTX.Homomorphisms', 697
  `MTX.InducedAction', 696
  `MTX.InducedActionFactorMatrix', 696
  `MTX.InducedActionFactorModule', 696
  `MTX.InducedActionMatrix', 696
  `MTX.InducedActionMatrixNB', 696
  `MTX.InducedActionSubmodule', 696
  `MTX.InducedActionSubmoduleNB', 696
  `MTX.InvariantBilinearForm', 697
  `MTX.InvariantQuadraticForm', 697
  `MTX.InvariantSesquilinearForm', 697
  `MTX.IsAbsolutelyIrreducible', 695
  `MTX.IsEquivalent', 697
  `MTX.IsIrreducible', 695
  `MTX.Isomorphism', 697
  `MTX.NormedBasisAndBaseChange', 696
  `MTX.OrthogonalSign', 697
  `MTX.ProperSubmoduleBasis', 695
  `MTX.SubGModule', 695
  `MTX.SubmoduleGModule', 695
  multiplication, 48
    \sub matrices, 223
    \sub matrix and matrix list, 224
    \sub matrix and scalar, 222
    \sub matrix and vector, 223
    \sub operation, 294
    \sub scalar and matrix, 222
    \sub scalar and matrix list, 224
    \sub scalar and vector, 214
    \sub vector and matrix, 223
    \sub vector and matrix list, 224
    \sub vector and scalar, 214
    \sub vectors, 214
  `MultiplicationTable', 319
  Multiplicative Arithmetic for Lists, \indexit{186}
  Multiplicative Arithmetic Functions, \indexit{142}
  `MultiplicativeNeutralElement', 321
  multiplicative order of an integer, 139
  `MultiplicativeZero', 321
  `MultiplicativeZeroOp', 291
  multiplicity, of constituents of a group character, 774
  multiplier, 380
  multisets, 195
  Multivariate Polynomials, \indexit{674}
  `MultRowVector', 217
  Murnaghan components, 786, 787
  Mutability and Copyability, \indexit{112}
  Mutability Status and List Arithmetic, \indexit{189}
  Mutable Bases, \indexit{603}
  `MutableBasis', 603
  `MutableBasisOfClosureUnderAction', 622
  `Mutable\-Basis\-Of\-Ideal\-In\-Nonassociative\-Algebra', 623
  `MutableBasisOfNonassociativeAlgebra', 623
  `MutableCopyMat', 227
  `MutableIdentityMat', 227
  `MutableNullMat', 227
\letter N
  $n_k$, 163
  `Name', 115
  `NameFunction', 61
  `NameRNam', 264
  `NamesFilter', 118
  `NamesGVars', 45
  `NamesLocalVariablesFunction', 61
  `NamesOfFusionSources', 805
  `NamesSystemGVars', 45
  `NamesUserGVars', 45
  `NaturalCharacter', 772
  Natural Embeddings related to Magma Rings, \indexit{662}
  `NaturalHomomorphismByGenerators', 307
  `NaturalHomomorphismByIdeal', 628
  `NaturalHomomorphismByNormalSubgroup', 370
  `NaturalHomomorphismByNormalSubgroupNC', 370
  `NaturalHomomorphismBySubAlgebraModule', 635
  `NaturalHomomorphismBySubspace', 608
  `NearAdditiveGroup', 556
  `NearAdditiveGroupByGenerators', 556
  `NearAdditiveMagma', 556
  `NearAdditiveMagmaByGenerators', 556
  `NearAdditiveMagmaWithZero', 556
  `NearAdditiveMagmaWithZeroByGenerators', 556
  `NearlyCharacterTablesFamily', 728
  negative number, 48
  `NegativeRoots', 644
  `NegativeRootVectors', 644
  `NestingDepthA', 184
  `NestingDepthM', 185
  `NewInfoClass', 80
  newline, 41
  newline character, 250
  `NewmanInfinityCriterion', 477
  New Presentations and Presentations for Subgroups, \indexit{472}
  `NextIterator', 276
  `NextPrimeInt', 132
  `NF', 590
  `NiceBasis', 610
  `NiceBasisFiltersInfo', 611
  `NiceFreeLeftModule', 610
  `NiceFreeLeftModuleInfo', 610
  `NiceMonomorphism', 387
  `NiceMonomorphismAutomGroup', 390
  Nice Monomorphisms, \indexit{387}
  `NiceObject', 387
  `NiceVector', 610
  `NilpotencyClassOfGroup', 364
  `NilpotentQuotientOfFpLieAlgebra', 651
  `NK', 163
  `NOAUTO', 843
  `NonabelianExteriorSquare', 380
  `NonnegativeIntegers', 126
  `NonnegIntScalarProducts', 812, 813
  `NonNilpotentElement', 649
  `Norm', 578
    \sub of character, 774
  `NormalBase', 580
  `NormalClosure', 360
  `NormalFormIntMat', 242
  Normal Forms of Integer Matrices - Name Changes, \indexit{847}
  Normal Forms over the Integers, \indexit{240}
  `NormalIntersection', 360
  `Normalized\-Element\-Of\-Magma\-Ring\-Modulo\-Relations', 663
  `NormalizedWhitespace', 254
  `Normalizer', 359
  normalizer, 359
  `NormalizerInGLnZ', 431
  `NormalizerInGLnZBravaisGroup', 431
  `NormalizersTom', 710
  `NormalizerTom', 710
  `NormalizeWhitespace', 254
  `NormalSeriesByPcgs', 444
  Normal Structure, \indexit{359}
  `NormalSubgroupClasses', 762
  `NormalSubgroupClassesInfo', 762
  `NormalSubgroups', 372
  `NormedRowVector', 215
  `NormedRowVectors', 607
  `NormedVectors', 847
  `not', 171
  `NrArrangements', 150
  `NrBasisVectors', 603
  `NrCombinations', 149
  `NrConjugacyClasses', 358
    \sub for character tables, 733
  `NrConjugacyClassesGL', 514
  `NrConjugacyClassesGU', 514
  `NrConjugacyClassesPGL', 514
  `NrConjugacyClassesPGU', 514
  `NrConjugacyClassesPSL', 514
  `NrConjugacyClassesPSU', 514
  `NrConjugacyClassesSL', 514
  `NrConjugacyClassesSLIsogeneous', 514
  `NrConjugacyClassesSU', 514
  `NrConjugacyClassesSUIsogeneous', 514
  `NrDerangements', 152
  `NrInputsOfStraightLineProgram', 337
  `NrMovedPoints', 411
  `NrOrderedPartitions', 154
  `NrPartitions', 153
  `NrPartitionsSet', 152
  `NrPartitionTuples', 155
  `NrPermutationsList', 151
  `NrPolyhedralSubgroups', 743
  `NrPrimitiveGroups', 525
  `NrRestrictedPartitions', 154
  `NrSubsTom', 706
  `NrTransitiveGroups', 516
  `NrTuples', 151
  `NrUnorderedTuples', 150
  `NullAlgebra', 617
  `NullMat', 226
  `NullspaceIntMat', 239
  `NullspaceMat', 228
  `NullspaceMatDestructive', 228
  `NullspaceModQ', 237
  `Number', 202
  number, Bell, 148
    \sub binomial, 147
    \sub Stirling, of the first kind, 148
    \sub Stirling, of the second kind, 149
  `NumberArgumentsFunction', 61
  `NumberFFVector', 216
  number field, 591
  number fields, Galois group, 594
  `NumberIrreducibleSolvableGroups', 527
  `NumberPerfectGroups', 521
  `NumberPerfectLibraryGroups', 521
  `NumberSmallGroups', 518
  `NumberSyllables', 333
  numerator, of a rational, 146
  `NumeratorOfModuloPcgs', 440
  `NumeratorOfRationalFunction', 669
  `NumeratorRat', 146
  Numerical Group Attributes, \indexit{366}
\letter O
  $O_p(G)$, see `PCore', 359
  `ObjByExtRep', 656
  Objects, \indexit{110}
  obsolete, 846
  `OCOneCocycles', 379
  octal character codes, 250
  `OctaveAlgebra', 616
  `od', 53
  `OldGeneratorsOfPresentation', 495
  `Omega', 363
  `ONanScottType', 415
  `OnBreak', 68
  `OnBreakMessage', 70
  `One', 290
  `OneAttr', 290
  `OneCoboundaries', 378
  `OneCocycles', 378
  one cohomology, 377
  `OneFactorBound', 676
  `OneImmutable', 290
  `OneIrreducibleSolvableGroup', 527
  `One<Library>Group', 516
  `OneMutable', 290
  `OneOfPcgs', 435
  `OneOp', 290
  `OnePrimitiveGroup', 516
  `OneSameMutability', 290
  `OneSM', 290
  `OneSmallGroup', 518
  `OneTransitiveGroup', 516
  `OnIndeterminates', 674
    \sub as a permutation action, 396
  `OnLeftInverse', 395
  `OnLines', 396
    \sub example, 511
  `OnPairs', 395
  `OnPoints', 395
  `OnRight', 395
  `OnSets', 395
  `OnSetsDisjointSets', 396
  `OnSetsSets', 395
  `OnSetsTuples', 396
  `OnSubspacesByCanonicalBasis', 397
  `OnTuples', 395
  `OnTuplesSets', 396
  `OnTuplesTuples', 396
  `Operation', 846
  `OperationAlgebraHomomorphism', 628
  Operational Structure of Domains, \indexit{284}
  `OperationHomomorphism', 846
  operations, for booleans, 170
  Operations and Attributes for Vector Spaces, \indexit{597}
  Operations applicable to All Streams, \indexit{98}
  Operations Concerning Blocks, \indexit{738}
  Operations for (Near-)Additive Magmas, \indexit{558}
  Operations for Abelian Number Fields, \indexit{590}
  operations for algebraic elements, 689
  Operations for Associative Words, \indexit{332}
  Operations for Associative Words by their Syllables, \indexit{333}
  Operations for Booleans, \indexit{170}
  Operations for Brauer Characters, \indexit{796}
  Operations for Class Functions, \indexit{773}
  Operations for Collections, \indexit{272}
  Operations for Cyclotomics, \indexit{157}
  Operations for Domains, \indexit{289}
  Operations for Finite Field Elements, \indexit{583}
  Operations for Finitely Presented Groups, \indexit{463}
  Operations for Group Homomorphisms, \indexit{384}
  Operations for Input Streams, \indexit{99}
  Operations for Lists, \indexit{197}
  Operations for Output Streams, \indexit{101}
  Operations for Pc Groups, \indexit{455}
  Operations for Rational Functions, \indexit{668}
  Operations for Special Kinds of Bases, \indexit{602}
  Operations for Stabilizer Chains, \indexit{421}
  Operations for Vector Space Bases, \indexit{600}
  Operations for Words, \indexit{325}
  Operations on elements of the algebra, \indexit{343}
  Operations on rewriting systems, \indexit{342}
  Operations to Evaluate Strings, \indexit{256}
  Operations to Produce or Manipulate Strings, \indexit{253}
  Operations which have Special Methods for Groups with Pcgs, \indexit{448}
  operators, 42
    \sub arithmetic, 48
    \sub associativity, 49
    \sub for cyclotomics, 161
    \sub for lists, 183
    \sub precedence, 48, 49
  Operators for Character Tables, \indexit{731}
  Operators for Matrices, \indexit{222}
  Operators for Row Vectors, \indexit{213}
  Optimization and Compiler Options, \indexit{835}
  options, 27, 827
    \sub command line, filenames, 29
    \sub command line, internal, 31
  options, under UNIX, 27
  `or', 170
  `Orbit', 397
  `OrbitFusions', 806
  `OrbitLength', 398
  `OrbitLengths', 398
  `OrbitLengthsDomain', 398
  `OrbitPerms', 413
  `OrbitPowerMaps', 801
  `Orbits', operation/attribute, 398
  Orbits, \indexit{397}
  `OrbitsDomain', 398
  `OrbitsPerms', 413
  `OrbitStabChain', 422
  `OrbitStabilizer', 399
  `OrbitStabilizerAlgorithm', 399
  Orbit Stabilizer Methods for Polycyclic Groups, \indexit{448}
  `Order', 293
    \sub of a class function, 770
  order,  of a group, 347
    \sub of a list, collection or domain, 271
    \sub of the prime residue group, 138
  `OrderedPartitions', 153
  ordering, booleans, 170
    \sub of records, 263
  `OrderingByLessThanFunctionNC', 278
  `OrderingByLessThanOrEqualFunctionNC', 278
  `OrderingOfRewritingSystem', 342
  `OrderingOnGenerators', 280
  `OrderingsFamily', 278
  Orderings on families of associative words, \indexit{280}
  `OrderMod', 139
  `OrderOfRewritingSystem', 342
  `OrdersClassRepresentatives', 734
  `OrdersTom', 706
  `Ordinal', 256
  ordinary character, 773
  `OrdinaryCharacterTable', 733
  `OrthogonalComponents', 786
  Orthogonal Embeddings, \indexit{246}
  `OrthogonalEmbeddings', 246
  `OrthogonalEmbeddingsSpecialDimension', 782
  OSX, 837
  Other Filters, \indexit{125}
  Other Operations Applicable to any Object, \indexit{115}
  Other Operations for Character Tables, \indexit{742}
  Other Operations for Tables of Marks, \indexit{710}
  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, 365
  package, 842
  Package Interface - Obsolete Functions and Name Changes, \indexit{846}
  Packages, \indexit{831}
  `PadicCoefficients', 244
  `PadicExtensionNumberFamily', 692
  `PadicNumber', 692
    \sub for pure padics, 691
  `PadicValuation', 567
  `Pager', 25
  `Parametrized', 809
  Parametrized Maps, \indexit{807}
  parametrized maps, 798
  `Parent', 288
  `ParentPcgs', 438
  Parents, \indexit{288}
  `PartialFactorization', 133
  partial order, 313
  `PartialOrderByOrderingFunction', 314
  `PartialOrderOfHasseDiagram', 313
  `Partitions', 153
  partitions, improper, of an integer, 154
    \sub ordered, of an integer, 154
    \sub restricted, of an integer, 154
  `PartitionsGreatestEQ', 154
  `PartitionsGreatestLE', 154
  `PartitionsSet', 152
  `PartitionTuples', 155
  `PcElementByExponents', 436
  `PcElementByExponentsNC', 436
  `PCentralLieAlgebra', 648
  `PCentralNormalSeriesByPcgsPGroup', 443
  `PCentralSeries', 369
  `PcGroupCode', 459
  `PcGroupCodeRec', 459
  `PcGroupFpGroup', 452
  Pc groups versus fp groups, \indexit{452}
  `PcGroupWithPcgs', 454
  `Pcgs', 434
  `Pcgs_OrbitStabilizer', 448
  Pcgs and Normal Series, \indexit{442}
  `PcgsByPcSequence', 434
  `PcgsByPcSequenceNC', 434
  `PcgsCentralSeries', 442
  `PcgsChiefSeries', 443
  `PcgsElementaryAbelianSeries', 442
  `PcgsPCentralSeriesPGroup', 443
  `PClassPGroup', 366
  `PCore', 359
  `PcSeries', 435
  `PerfectGroup', 520
  perfect groups, 520
  `PerfectIdentification', 521
  `PerfectResiduum', 361
  `Perform', 199
  `Permanent', 156
  Permanent of a Matrix, \indexit{156}
  `PermBounds', 795
  `PermCharInfo', 790
  `PermCharInfoRelative', 791
  `PermChars', 792
  `PermCharsTom', 719
  `PermComb', 795
  `PermLeftQuoTransformation', 554
  `PermList', 412
  `PermListList', 199
  `Permutation', 403
  `PermutationCharacter', 773
  permutation character, 818
  permutation characters, possible, 789, 792
  `PermutationCycle', 403
  `PermutationCycleOp', 403
  `PermutationMat', 226
  `PermutationsFamily', 409
  Permutations Induced by Elements and Cycles, \indexit{403}
  `PermutationsList', 151
  `PermutationTom', 705
  `Permuted', 201
    \sub as a permutation action, 397
    \sub for class functions, 770
  `PGL', 513
  `PGU', 513
  `Phi', 138
  point stabilizer, 399
  Polycyclic Generating Systems, \indexit{433}
  `PolynomialByExtRep', 687
  `PolynomialByExtRepNC', 687
  `PolynomialCoefficientsOfPolynomial', 672
  `PolynomialDivisionAlgorithm', 683
  Polynomial Factorization, \indexit{675}
  `PolynomialModP', 675
  `PolynomialReducedRemainder', 683
  `PolynomialReduction', 682
  `PolynomialRing', 678
  Polynomial Rings, \indexit{678}
  Polynomials as Univariate Polynomials in one Indeterminate, \indexit{672}
  polynomials over abelian number fields, factors, 590
  Polynomials over the Rationals, \indexit{675}
  `PopOptions', 88
  Portability, \indexit{90}
  Porting GAP, \indexit{836}
  `Position', 190
  `PositionBound', 192
  `PositionCanonical', 190
  `PositionFirstComponent', 192
  `PositionNonZero', 192
  `PositionNot', 192
  `PositionNthOccurrence', 190
  `PositionProperty', 192
  `Positions', 190
  `PositionSet', 191
  `PositionsOp', 190
  `PositionSorted', 191
  `PositionStream', 100
  `PositionSublist', 192
  `PositionWord', 332
  `PositiveIntegers', 126
  positive number, 48
  `PositiveRoots', 644
  `PositiveRootVectors', 644
  `PossibleClassFusions', 805
  `PossibleFusionsCharTableTom', 718
  Possible Permutation Characters, \indexit{789}
  possible permutation characters, 789, 792
  `PossiblePowerMaps', 799
  power, 48
    \sub matrix, 223
    \sub meaning for class functions, 769
    \sub of words, 332
  `PowerMap', 799
  `PowerMapByComposition', 801
  `PowerMapOp', 799
  Power Maps, \indexit{798}
  `PowerMapsAllowedBySymmetrizations', 816
  `PowerMod', 569
  `PowerModCoeffs', 219
  `PowerModInt', 131
  `PowerPartition', 155
  powerset, 149
  `PowerSubalgebraSeries', 621
  `PQuotient', 474
  precedence, 48
  precedence test, for permutations, 410
  `PrefrattiniSubgroup', 361
    \sub for groups with pcgs, 448
  `PreImage', 306
  `PreImageElm', 306
  `PreImages', 306
  `PreImagesElm', 305
  Preimages in the Free Group, \indexit{462}
  Preimages in the Free Semigroup, \indexit{548}
  `PreimagesOfTransformation', 553
  `PreImagesRange', 305
  `PreImagesRepresentative', 306
  `PreImagesSet', 306
  Preimages under Homomorphisms from an FpGroup, \indexit{473}
  Preimages under Mappings, \indexit{305}
  preorder, 313
  `PresentationFpGroup', 479
  `PresentationNormalClosure', 484
  `PresentationNormalClosureRrs', 484
  `PresentationSubgroup', 482
  `PresentationSubgroupMtc', 483
  `PresentationSubgroupRrs', 482
  `PresentationViaCosetTable', 480
  previous result, 64
  `PrevPrimeInt', 132
  `PrimaryGeneratorWords', 483
  primary subgroup generators, 497
  `PrimeBlocks', 738
  `PrimeBlocksOp', 738
  `PrimeField', 577
  Prime Integers and Factorization, \indexit{131}
  `PrimePGroup', 366
  `PrimePowersInt', 134
  prime residue group, 138
    \sub exponent, 139
    \sub generator, 140
    \sub order, 138
  Prime Residues, \indexit{138}
  `PrimeResidues', function, 138
  `Primes', 131
  primitive, 405
  `PRIMITIVE_INDICES_MAGMA', 526
  `PrimitiveElement', 577
  `PrimitiveGroup', 525
  Primitive Groups, \indexit{415}
  `PrimitiveGroupsIterator', 525
  `PrimitiveIdentification', 526
  `PrimitiveIndexIrreducibleSolvableGroup', 527
  Primitive Permutation Groups, \indexit{524}
  `PrimitivePolynomial', 675
  `PrimitiveRoot', 585
  `PrimitiveRootMod', 140
  primitive root modulo an integer, 140
  Primitive Roots and Discrete Logarithms, \indexit{139}
  Primitivity of Characters, \indexit{821}
  `Print', 66
  `PrintAmbiguity', 812
  `PrintArray', 227
  `PrintCharacterTable', 747
  `PrintFactorsInt', 134
  `PrintFormattingStatus', 102
  Printing, Viewing and Displaying Finite Field Elements, \indexit{587}
  Printing Character Tables, \indexit{744}
  Printing Class Functions, \indexit{770}
  Printing Presentations, \indexit{485}
  Printing Tables of Marks, \indexit{703}
  `PrintObj', 67
    \sub for character tables, 744, 770
    \sub for tables of marks, 703
  `PrintTo', 95
    \sub for streams, 101
  `ProbabilityShapes', 676
  problems, 833
  Problems on Particular Systems, \indexit{835}
  procedure call, 50
  Procedure Calls, \indexit{50}
  procedure call with arguments, 50
  `Process', 108
  Process, \indexit{108}
  `PROD_GF2MAT_GF2MAT_ADVANCED', 237
  `PROD_GF2MAT_GF2MAT_SIMPLE', 237
  `Product', 203
  product, of words, 332
    \sub rational functions, 668
  `ProductCoeffs', 219
  `ProductOfStraightLinePrograms', 340
  `ProductSpace', 621
  `ProductX', 206
  `ProfileFunctions', 83
  `ProfileGlobalFunctions', 83
  `ProfileMethods', 82
  `ProfileOperations', 82
  `ProfileOperationsAndMethods', 82
  `PROFILETHRESHOLD', 83
  Profiling, \indexit{82}
  `ProjectedInducedPcgs', 441
  `ProjectedPcElement', 441
  `Projection', 303
    \sub example for direct products, 502
    \sub example for semidirect products, 504
    \sub example for subdirect products, 505
    \sub example for wreath products, 505
    \sub for group products, 507
  `ProjectionMap', 808
  projections, find all, 391
  `ProjectiveActionHomomorphismMatrixGroup', 428
  `ProjectiveActionOnFullSpace', 428
  `ProjectiveGeneralLinearGroup', 513
  `ProjectiveGeneralUnitaryGroup', 513
  `ProjectiveOrder', 236
  `ProjectiveSpecialLinearGroup', 513
  `ProjectiveSpecialUnitaryGroup', 513
  `ProjectiveSymplecticGroup', 513
  prompt, 64
    \sub partial, 64
  Properties, \indexit{124}
  Properties and Attributes for Lists, \indexit{193}
  Properties and Attributes of (General) Mappings, \indexit{303}
  Properties and Attributes of Binary Relations, \indexit{312}
  Properties and Attributes of Matrices, \indexit{224}
  Properties and Attributes of Rational Functions, \indexit{669}
  Properties and basic functionality, \indexit{279}
  Properties of a Lie Algebra, \indexit{642}
  Properties of rewriting systems, \indexit{344}
  Properties of Rings, \indexit{564}
  Properties of Tables of Marks, \indexit{709}
  `PRump', 362
  `PseudoRandom', 275
  `PSL', 513
  `PSP', 513
  `PSp', 513
  `PSU', 513
  `PthPowerImage', 648
  `PthPowerImages', 648
  Pure p-adic Numbers, \indexit{691}
  `PurePadicNumberFamily', 691
  `PushOptions', 88
\letter Q
  `Quadratic', 164
  quadratic residue, 141
  `QuaternionAlgebra', 616
  `QUIET', 847
  `QUIT', emergency quit, 73
  quit, in emergency, 73
  `quit', 68
  `QUITTING', 73
  `QuoInt', 129
  `Quotient', 560
  quotient, for finitely presented groups, 461
    \sub matrices, 223
    \sub matrix and matrix list, 224
    \sub matrix and scalar, 223
    \sub of free monoid, 549
    \sub of free semigroup, 547
    \sub of words, 332
    \sub rational functions, 668
    \sub scalar and matrix, 223
    \sub scalar and matrix list, 224
    \sub vector and matrix, 223
  `QuotientFromSCTable', 615
  Quotient Methods, \indexit{474}
  `QuotientMod', 569
  `QuotientPolynomialsExtRep', 688
  `QuotientRemainder', 568
  Quotients, \indexit{539}
  Quotients and Remainders, \indexit{129}
  `QuotientSemigroupCongruence', 539
  `QuotientSemigroupHomomorphism', 539
  `QuotientSemigroupPreimage', 539
  `QuotRemLaurpols', 677
\letter R
  $r_N$, 162
  `RadicalGroup', 361
  `RadicalOfAlgebra', 624
  `Random', 136
    \sub `[coll]', 274
    \sub for integers, 129
    \sub for rationals, 146
  `RandomBinaryRelationOnPoints', 314
  random element, of a list or collection, 274
  Random Elements, \indexit{274}
  `RandomInvertibleMat', 228
  `RandomIsomorphismTest', 459
  Random Isomorphism Testing, \indexit{459}
  Randomized Methods for Permutation Groups, \indexit{417}
  `RandomList', 275
  `RandomMat', 228
  Random Matrices, \indexit{228}
  `RandomPrimitivePolynomial', 587
  random seed, 275
  `RandomSource', 137
  Random Sources, \indexit{136}
  `RandomTransformation', 552
  `RandomUnimodularMat', 228
  `Range', 304
  range, 206
  Ranges, \indexit{206}
  `RankAction', 404
  `RankFilter', 117
  `RankMat', 228
  `RankOfTransformation', 553
  `RankPGroup', 366
  `Rat', 146
    \sub for strings, 256
  `RationalClass', 358
  `RationalClasses', 359
  `RationalFunctionByExtRep', 687
  `RationalFunctionByExtRepNC', 687
  `Rational\-Function\-By\-Ext\-Rep\-With\-Cancellation', 688
  Rational Function Families, \indexit{684}
  `RationalFunctionsFamily', 684
  `RationalizedMat', 165
  `Rationals', 145
  `RClassOfHClass', 540
  `Read', 94
    \sub for streams, 99
  `ReadAll', 100
  `ReadAllLine', 106
  `ReadAsFunction', 94
    \sub for streams, 99
  `ReadByte', 99
  read eval print loop, 64
  `ReadLine', 99
  `ReadPackage', 843
  `ReadPkg', 846
  `ReadTest', 84
    \sub for streams, 99
  `RealClasses', 736
  `RealizableBrauerCharacters', 796
  `RecNames', 259
  Recognizing Characters, \indexit{252}
  record, component access, 260
    \sub component assignment, 260
    \sub component variable, 260
    \sub component variable assignment, 261
  Record Access Operations, \indexit{264}
  Record Assignment, \indexit{260}
  record assignment, operation, 264
  record boundness test, operation, 264
  record component, operation, 264
  record unbind, operation, 264
  Recovery from NoMethodFound-Errors, \indexit{77}
  recursion, 55
  redisplay a help section, 23
  redisplay with next help viewer, 23
  `ReduceCoeffs', 219
  `ReduceCoeffsMod', 219
  `ReducedAdditiveInverse', 343
  `ReducedCharacters', 780
  `ReducedClassFunctions', 779
  `ReducedComm', 343
  `ReducedConfluentRewritingSystem', 550
  `ReducedConjugate', 343
  `ReducedDifference', 343
  `ReducedForm', 342
  `ReducedGroebnerBasis', 684
  `ReducedInverse', 343
  `ReducedLeftQuotient', 343
  `ReducedOne', 343
  `ReducedPcElement', 436
  `ReducedPower', 343
  `ReducedProduct', 343
  `ReducedQuotient', 343
  `ReducedScalarProduct', 343
  `ReducedSum', 343
  `ReducedZero', 343
  `ReduceRules', 343
  `ReduceStabChain', 423
  Reducing Virtual Characters, \indexit{779}
  `Ree', 510
  `ReeGroup', 510
  `ReesCongruenceOfSemigroupIdeal', 538
  `ReesMatrixSemigroup', 541
  `ReesMatrixSemigroupElement', 542
  Rees Matrix Semigroups, \indexit{541}
  `ReesZeroMatrixSemigroup', 541
  `ReesZeroMatrixSemigroupElement', 542
  `ReesZeroMatrixSemigroupElementIsZero', 542
  `RefinedPcGroup', 454
  `ReflectionMat', 227
  `ReflexiveClosureBinaryRelation', 314
  reflexive relation, 312
  regular, 404
  regular action, 401
  `RegularActionHomomorphism', 402
  `RegularModule', 750
  relations, 301
  Relations Between Domains, \indexit{295}
  `RelationsOfFpSemigroup', 548
  `RelativeBasis', 600
  `RelativeBasisNC', 600
  relatively prime, 48
  `RelativeOrderOfPcElement', 436
  `RelativeOrders', of a pcgs, 435
  Relators in a Presentation, \indexit{485}
  `RelatorsOfFpGroup', 462
  remainder, operation, 294
  remainder of a quotient, 129
  `RemInt', 129
  `Remove', 177
  remove, an element from a set, 196
  `RemoveFile', 96
  `RemoveOuterCoeffs', 217
  `RemoveRelator', 487
  `RemoveSet', 196
  `RemoveStabChain', 423
  Repeat, \indexit{52}
  `repeat' loop, 52
  `ReplacedString', 254
  Representation, \indexit{120}
  representation, as a sum of two squares, 144
  Representations for Associative Words, \indexit{334}
  Representations for Group Homomorphisms, \indexit{393}
  Representations given by modules, \indexit{750}
  Representations of Algebras, \indexit{629}
  `RepresentationsOfObject', 121
  `Representative', 271
  representative, of a list or collection, 272
  `RepresentativeAction', 400
  `RepresentativeLinearOperation', 629
  `RepresentativeOperation', 846
  `RepresentativesContainedRightCosets', 356
  `RepresentativesFusions', 806
  `RepresentativeSmallest', 272
  `RepresentativesMinimalBlocks', 405
  `RepresentativesPerfectSubgroups', 374
  `RepresentativesPowerMaps', 801
  `RepresentativesSimpleSubgroups', 374
  `RepresentativeTom', 717
  `RepresentativeTomByGenerators', 717
  `RepresentativeTomByGeneratorsNC', 717
  `RequirePackage', 846
  `Reread', 96
  `REREADING', 96
  `RereadPackage', 843
  `RereadPkg', 846
  `Reset', 136
  `ResetOptionsStack', 88
  residue, quadratic, 141
  Residue Class Rings, \indexit{134}
  `RespectsAddition', 309
  `RespectsAdditiveInverses', 309
  `RespectsInverses', 308
  `RespectsMultiplication', 308
  `RespectsOne', 308
  `RespectsScalarMultiplication', 309
  `RespectsZero', 309
  `RestoreStateRandom', 274
  Restricted and Induced Class Functions, \indexit{777}
  `RestrictedClassFunction', 778
  `RestrictedClassFunctions', 778
  Restricted Lie algebras, \indexit{647}
  `RestrictedMapping', 303
  `RestrictedPartitions', 154
  `RestrictedPerm', 412
  `RestrictedPermNC', 412
  `RestrictedTransformation', 553
  `RestrictOutputsOfSLP', 339
  `Resultant', 673
  `ResultOfStraightLineProgram', 337
  Return, \indexit{58}
  `return', 68
    \sub no value, 58
    \sub with value, 58
  `ReturnFail', 63
  `ReturnFalse', 63
  return from break loop, 68
  `ReturnTrue', 63
  `Reversed', 199
  `RewindStream', 101
  `RewriteWord', 468
  Rewriting in Groups and Monoids, \indexit{344}
  Rewriting Systems and the Knuth-Bendix Procedure, \indexit{550}
  `RightActingAlgebra', 632
  `RightActingRingOfIdeal', 563
  `RightAlgebraModule', 630
  `RightAlgebraModuleByGenerators', 630
  `RightCoset', 354
  `RightCosets', 355
  right cosets, 354
  `RightCosetsNC', 355
  `RightDerivations', 639
  `RightIdeal', 561
  `RightIdealByGenerators', 562
  `RightIdealNC', 562
  `RightModuleByHomomorphismToMatAlg', 633
  `RightShiftRowVector', 217
  `RightTransversal', 355
  `Ring', 559
  `RingByGenerators', 560
  Ring Homomorphisms, \indexit{310}
  Rings With One, \indexit{563}
  `RingWithOne', 563
  `RingWithOneByGenerators', 564
  `RNamObj', 264
  root, of 1 modulo an integer, 142
    \sub of an integer, 128
    \sub of an integer, smallest, 128
    \sub of an integer modulo another, 141
  `RootInt', 128
  `RootMod', 141
  `RootOfDefiningPolynomial', 577
  `RootsMod', 141
  Roots Modulo Integers, \indexit{140}
  roots of unity, 157
  `RootsOfUPol', 672
  `RootsUnityMod', 142
  `RootSystem', 644
  `RoundCyc', 159
  Row and Matrix Spaces, \indexit{604}
  `RowIndexOfReesMatrixSemigroupElement', 542
  `Row\-Index\-Of\-Rees\-Zero\-Matrix\-Semigroup\-Element', 542
  row spaces, 604
  Row Vectors over Finite Fields, \indexit{215}
  `Rules', 342
  Running GAP under MacOS, \indexit{31}
  `Runtime', 82
  `Runtimes', 81
\letter S
  $s_N$, 162
  `SameBlock', 739
  `SandwichMatrixOfReesMatrixSemigroup', 542
  `SandwichMatrixOfReesZeroMatrixSemigroup', 542
  save, 37
  `SaveOnExitFile', 73
  `SaveWorkspace', 37
  Saving and Loading a Workspace, \indexit{37}
  Saving a Pc Group, \indexit{455}
  saving on exit, 73
  `ScalarProduct', for characters, 774
  Schreier, 482
  Schreier-Sims, random, 417
  `SchurCover', 380
  Schur Covers and Multipliers, \indexit{380}
  Schur multiplier, 380
  scope, 43
  `ScriptFromString', 714
  Searching for Homomorphisms, \indexit{391}
  `SecHMSM', 258
  secondary subgroup generators, 497
  `SecondsDMYhms', 258
  `SeekPositionStream', 101
  Selecting a Different MeatAxe, \indexit{695}
  Selection Functions, \indexit{515}
  `SemidirectProduct', 503
  Semidirect Products, \indexit{503}
  `SemiEchelonBasis', 606
  `SemiEchelonBasisNC', 606
  `SemiEchelonMat', 230
  `SemiEchelonMatDestructive', 231
  `SemiEchelonMats', 231
  `SemiEchelonMatsDestructive', 231
  `SemiEchelonMatTransformation', 231
  `Semigroup', 536
  semigroup, 536
  `SemigroupByGenerators', 536
  `SemigroupByMultiplicationTable', 537
  `SemigroupIdealByGenerators', 538
  `SemigroupOfRewritingSystem', 551
  semiregular, 404
  Semisimple Lie Algebras and Root Systems, \indexit{643}
  `SemiSimpleType', 643
  sequence, Bernoulli, 148
    \sub Fibonacci, 155
    \sub Lucas, 156
  Series of Ideals, \indexit{641}
  `Set', 268
  `SetAssertionLevel', 81
  `SetCommutator', 453
  `SetConjugate', 453
  `SetCrystGroupDefaultAction', 432
  set difference, of collections, 273
  `SetEntrySCTable', 614
  `SetGasmanMessageStatus', 87
  `SetHelpViewer', 24
  `SetIndeterminateName', 667
  `SetInfoLevel', 80
  `SetName', 115
  Set Operations via Boolean Lists, \indexit{210}
  `SetParent', 288
  `SetPower', 453
  `SetPrintFormattingStatus', 102
  `SetRecursionTrapInterval', 86
  `SetReducedMultiplication', 462
  Sets, \indexit{111}
  sets, 172, 195
  Sets of Subgroups, \indexit{371}
  set stabilizer, 399
  `Setter', 122
  setter, 122
  Setter and Tester for Attributes, \indexit{122}
  `SetX', 206
  `ShallowCopy', 114
    \sub for lists, 180
  `ShiftedCoeffs', 219
  `ShiftedPadicNumber', 691
  Shifting and Trimming Coefficient Lists, \indexit{217}
  `ShortestVectors', 246
  `ShortLexOrdering', 281
  short vectors spanning a lattice, 244, 780
  `ShowArgument', 77
  `ShowArguments', 77
  `ShowDetails', 77
  `ShowImpliedFilters', 118
  `ShowMethods', 78
  `ShowOtherMethods', 78
  `ShrinkCoeffs', 220
  `ShrinkRowVector', 217
  `SiftedPcElement', 436
  `SiftedPermutation', 422
  `SiftedVector', 607
  `Sigma', 142
  sign, of an integer, 127
  Sign and Cycle Structure, \indexit{411}
  `SignInt', 127
  `SignPartition', 154
  `SignPerm', 411
  `SimpleLieAlgebra', 639
  `SimpleSystem', 644
  `SimplifiedFpGroup', 481
  SimplifiedFpGroup, \indexit{481}
  `SimplifyPresentation', 488
  `SimsNo', 526
  `SimultaneousEigenvalues', 237
  `SingleCollector', 453
  singlequote character, 250
  singlequotes, 248
  `SINT_CHAR', 255
  `Size', 271
    \sub for character tables, 733
    \sub for groups with pcgs, 448
  size, of a list or collection, 271
  `SizeBlist', 210
  `SizeConsiderFunction', 376
  `SizeNumbersPerfectGroups', 521
  `SizeOfFieldOfDefinition', 796
  `SizesCentralizers', 734
  `SizesConjugacyClasses', 734
  `SizeScreen', 76
  SizeScreen, \indexit{76}
  `SizesPerfectGroups', 520
  `SizeStabChain', 421
  `SL', 511
  smaller, associative words, 331
    \sub elements of finitely presented groups, 462
    \sub nonassociative words, 325
    \sub pcwords, 451
    \sub rational functions, 669
  `SmallerDegreePermutationRepresentation', 414
  smaller or equal, 47
  smaller test, 47
  `SmallestGeneratorPerm', 410
  `SmallestMovedPoint', 410
  `SmallestRootInt', 128
  `SmallGeneratingSet', 377
  `SmallGroup', 518
  Small Groups, \indexit{517}
  `SmallGroupsInformation', 519
  Smash MeatAxe Flags, \indexit{699}
  smith normal form, 847
  `SmithNormalFormIntegerMat', 241
  `SmithNormalFormIntegerMatTransforms', 241
  `SMTX.AbsoluteIrreducibilityTest', 698
  `SMTX.AlgEl', 699
  `SMTX.AlgElCharPol', 699
  `SMTX.AlgElCharPolFac', 699
  `SMTX.AlgElMat', 699
  `SMTX.AlgElNullspaceDimension', 699
  `SMTX.AlgElNullspaceVec', 699
  `SMTX.CentMat', 699
  `SMTX.CentMatMinPoly', 699
  `SMTX.CompleteBasis', 698
  `SMTX.Getter', 698
  `SMTX.GoodElementGModule', 698
  `SMTX.IrreducibilityTest', 698
  `SMTX.MatrixSum', 698
  `SMTX.MinimalSubGModule', 698
  `SMTX.MinimalSubGModules', 698
  `SMTX.RandomIrreducibleSubGModule', 698
  `SMTX.Setter', 698
  `SMTX.SortHomGModule', 698
  `SMTX.Subbasis', 699
  `SO', 512
  `Socle', 362
  `SocleTypePrimitiveGroup', 415
  `SolutionIntMat', 239
  `SolutionMat', 229
  `SolutionMatDestructive', 229
  `SolutionNullspaceIntMat', 239
  Some Remarks about Character Theory in GAP, \indexit{722}
  Some Special Algebras, \indexit{616}
  `Sort', 194
  `SortedCharacters', 758
  `SortedCharacterTable', 758
  Sorted Character Tables, \indexit{757}
  `SortedList', 268
  sorted list, 193
  Sorted Lists and Sets, \indexit{195}
  sorted lists as collections, 266
  `SortedSparseActionHomomorphism', 401
  `SortedTom', 704
  `Sortex', 194
  Sorting Lists, \indexit{194}
  `SortingPerm', 195
  Sorting Tables of Marks, \indexit{704}
  `SortParallel', 194
  `Source', 304
  `SourceOfIsoclinicTable', 756
  `SP', 512
  `Sp', 512
  space, 41
  `SparseActionHomomorphism', 401
  `SparseCartanMatrix', 645
  Special Characters, \indexit{250}
  special character sequences, 250
  Special Filenames, \indexit{93}
  Special Generating Sets, \indexit{377}
  `SpecialLinearGroup', 511
  Special Multiplication Algorithms for Matrices over GF(2), \indexit{237}
  `SpecialOrthogonalGroup', 512
  Special Pcgs, \indexit{445}
  `SpecialPcgs', attribute, 445
  Special Rules for Input Lines, \indexit{65}
  `SpecialUnitaryGroup', 512
  Specific and Parametrized Subgroups, \indexit{360}
  Specific Methods for Subgroup Lattice Computations, \indexit{374}
  `SplitCharacters', 752
  `SplitExtension', 457
  `SplitExtensions', 458
  `SplitString', 253
  `SplittingField', 671
  `Sqrt', 294
  square root, of an integer, 128
  `SquareRoots', 322
  `SSortedList', 268
  `StabChain', 419
  `StabChainBaseStrongGenerators', 420
  `StabChainImmutable', 419
  `StabChainMutable', 419
  `StabChainOp', 419
  `StabChainOptions', 420
  `Stabilizer', 399
  Stabilizer Chain Records, \indexit{420}
  Stabilizer Chains, \indexit{416}
  `StabilizerOfExternalSet', 407
  `StabilizerPcgs', 448
  Stabilizers, \indexit{399}
  `StandardAssociate', 566
  `StandardGeneratorsFunctions', 714
  `StandardGeneratorsInfo', for groups, 713
    \sub for tables of marks, 718
  `StandardGeneratorsOfGroup', 715
  Standard Generators of Groups, \indexit{713}
  Standardization of coset tables, \indexit{467}
  `StandardizeTable', 467
  `StarCyc', 164
  `State', 136
  Statements, \indexit{49}
  `StateRandom', 274
  `Stirling1', 148
  `Stirling2', 149
  Stirling number of the first kind, 148
  Stirling number of the second kind, 149
  `StoredGroebnerBasis', 684
  `StoreFusion', 804
  Storing Normal Subgroup Information, \indexit{762}
  `StraightLineProgElm', 340
  `StraightLineProgGens', 341
  `StraightLineProgram', 336
  Straight Line Program Elements, \indexit{340}
  `StraightLineProgramNC', 336
  Straight Line Programs, \indexit{336}
  `StraightLineProgramsTom', 716
  `StreamsFamily', 98
  `StretchImportantSLPElement', 341
  strictly sorted list, 193
  `String', 253
    \sub for cyclotomics, 159
  `StringDate', 257
  `StringOfResultOfStraightLineProgram', 338
  `StringPP', 253
  strings, equality of, 252
    \sub inequality of, 252
    \sub lexicographic ordering of, 252
  String Streams, \indexit{104}
  `StringTime', 258
  `StrongGeneratorsStabChain', 421
  `StronglyConnectedComponents', 314
  <Struct>, 285
  `<Struct>ByGenerators', 286
  `StructuralCopy', 114
    \sub for lists, 180
  structure constant, 743, 744
  `StructureConstantsTable', 602
  `StructureDescription', 352
  Structure Descriptions, \indexit{352}
  `<Struct>WithGenerators', 286
  `SU', 512
  `Subalgebra', 617
  `SubAlgebraModule', 633
  `SubalgebraNC', 617
  Subalgebras, \indexit{617}
  `SubalgebraWithOne', 617
  `SubalgebraWithOneNC', 618
  `SubdirectProduct', 505
  Subdirect Products, \indexit{505}
  `SubdirectProducts', 505
  subdomains, 289
  `Subfield', 577
  `SubfieldNC', 577
  `Subfields', 577
  Subfields of Fields, \indexit{577}
  `Subgroup', 349
  `SubgroupByPcgs', 439
  `SubgroupByProperty', 350
  subgroup fusions, 802
  subgroup generators tree, 497
  Subgroup Lattice, \indexit{372}
  `SubgroupNC', 349
  `SubgroupOfWholeGroupByCosetTable', 468
  `SubgroupOfWholeGroupByQuotientSubgroup', 473
  Subgroup Presentations, \indexit{482}
  `SubgroupProperty', 424
  Subgroups, \indexit{349}
  subgroups, polyhedral, 743
  Subgroups characterized by prime powers, \indexit{363}
  Subgroup Series, \indexit{367}
  `SubgroupShell', 350
  Subgroups of Polycyclic Groups - Canonical Pcgs, \indexit{439}
  Subgroups of Polycyclic Groups - Induced Pcgs, \indexit{438}
  `SubgroupsSolvableGroup', 375
  sublist, 174
    \sub access, 174
    \sub assignment, 176
    \sub operation, 175
  sublist assignment, operation, 177
  `Submagma', 318
  `SubmagmaNC', 318
  `SubmagmaWithInverses', 318
  `SubmagmaWithInversesNC', 318
  `SubmagmaWithOne', 318
  `SubmagmaWithOneNC', 318
  `Submodule', 572
  `SubmoduleNC', 572
  Submodules, \indexit{572}
  `Submonoid', 543
  `SubmonoidNC', 543
  `SubnearAdditiveGroup', 557
  `SubnearAdditiveGroupNC', 557
  `SubnearAdditiveMagma', 557
  `SubnearAdditiveMagmaNC', 557
  `SubnearAdditiveMagmaWithZero', 557
  `SubnearAdditiveMagmaWithZeroNC', 557
  `SubnormalSeries', 367
  `Subring', 560
  `SubringNC', 560
  `SubringWithOne', 564
  `SubringWithOneNC', 564
  Subroutines for the Construction of Class Fusions, \indexit{817}
  Subroutines for the Construction of Power Maps, \indexit{815}
  `Subsemigroup', 536
  `SubsemigroupNC', 536
  subsets, 149
  subset test, for collections, 272
  `Subspace', 596
  `SubspaceNC', 596
  `Subspaces', 598
  `SubstitutedWord', 333
  `SubsTom', 706
  `Sub<struct>', 289
  `Sub<struct>NC', 289
  `SubSyllables', 334
  subtract, a set from another, 197
  `SubtractBlist', 211
  subtraction, 48
    \sub matrices, 222
    \sub matrix and scalar, 222
    \sub rational functions, 668
    \sub scalar and matrix, 222
    \sub scalar and matrix list, 224
    \sub scalar and vector, 214
    \sub vector and scalar, 214
    \sub vectors, 214
  `SubtractSet', 197
  `Subword', 332
  `Successors', 313
  Suitability for Compilation, \indexit{36}
  `Sum', 204
  Sum and Intersection of Pcgs, \indexit{444}
  `SumFactorizationFunctionPcgs', 444
  `SumIntersectionMat', 232
  `SumX', 206
  `SupersolvableResiduum', 362
  `support', email address, 834
  `SupportedCharacterTableInfo', 726
  `SurjectiveActionHomomorphismAttr', 408
  `SuzukiGroup', 510
  `SylowComplement', 362
  `SylowSubgroup', 362
  Sylow Subgroups and Hall Subgroups, \indexit{362}
  `SylowSystem', 363
  Symbols, \indexit{40}
  Symmetric and Alternating Groups, \indexit{414}
  `SymmetricClosureBinaryRelation', 314
  `SymmetricGroup', 510
  symmetric group, powermap, 155
  `SymmetricParentGroup', 415
  `SymmetricParts', 786
  `SymmetricPowerOfAlgebraModule', 658
  symmetric relation, 313
  `Symmetrizations', 785
  symmetrizations, orthogonal, 786, 787
    \sub symplectic, 787
  Symmetrizations of Class Functions, \indexit{785}
  `SymplecticComponents', 787
  `SymplecticGroup', 512
  syntax errors, 64
  system getter, 121
  system setter, 121
  `Sz', 510
\letter T
  $t_N$, 162
  `TableAutomorphisms', 760
  table automorphisms, 806, 818
  table of chapters for help books, 23
  `TableOfMarks', 701
  `TableOfMarksByLattice', 702
  `TableOfMarksComponents', 705
  `TableOfMarksCyclic', 720
  `TableOfMarksDihedral', 720
  `TableOfMarksFamily', 705
  `TableOfMarksFrobenius', 720
  Table of Marks Objects in GAP, \indexit{701}
  table of sections for help books, 23
  tables, 722, 724
  tabulator, 41
  `Tau', 142
  Technical Details about Tables of Marks, \indexit{705}
  Technical Details about the Implementation of Magma Rings, \indexit{664}
  Technical Matters Concerning General Mappings, \indexit{310}
  `TemporaryGlobalVarName', 46
  `Tensored', 777
  `TensorProductGModule ', 694
  `TensorProductOfAlgebraModules', 657
  Tensor Products and Exterior and Symmetric Powers, \indexit{657}
  test, for a primitive root, 140
    \sub for a rational, 145
    \sub for records, 259
    \sub for set equality, 196
  `TestConsistencyMaps', 811
  `Tester', 122
  tester, 122
  Test Files, \indexit{84}
  `TestHomogeneous', 821
  `TestInducedFromNormalSubgroup', 823
  Testing Finiteness of Finitely Presented Groups, \indexit{477}
  Testing for the System Architecture, \indexit{35}
  Testing Monomiality, \indexit{823}
  `TestJacobi', 614
  `TestMonomial', 823
  `TestMonomialQuick', 824
  `TestMonomialUseLattice', 824
  Test of the installation, \indexit{830}
  `TestPackageAvailability', 844
  `TestPerm1', 793
  `TestPerm2', 793
  `TestPerm3', 793
  `TestPerm4', 793
  `TestPerm5', 793
  `TestQuasiPrimitive', 822
  `TestRelativelySM', 825
  Tests for Actions, \indexit{404}
  Tests for the Availability of Methods, \indexit{381}
  `TestSubnormallyMonomial', 825
  The .gaprc file, \indexit{33}
  The Adjoint Representation, \indexit{649}
  The Compiler, \indexit{35}
  The Defining Attributes of Rational Functions, \indexit{686}
  The Dixon-Schneider Algorithm, \indexit{751}
  The Documentation, \indexit{832}
  The External Representation for Associative Words, \indexit{336}
  The family pcgs, \indexit{451}
  The Interface between Character Tables and Groups, \indexit{728}
  The Interface between Tables of Marks and Character Tables, \indexit{718}
  The Library of Tables of Marks, \indexit{721}
  `then', 51
  The Natural Action, \indexit{413}
  The Pager Command, \indexit{25}
  The Permutation Image of an Action, \indexit{400}
  The Representations of Rational Functions, \indexit{685}
  The Smash MeatAxe, \indexit{698}
  The Syntax in BNF, \indexit{59}
  `ThreeGroup' library, 518
  Tietze Options, \indexit{500}
  Tietze Transformations, \indexit{487}
  Tietze Transformations that introduce new Generators, \indexit{492}
  `TietzeWordAbstractWord', 485
  `time', 82
  Timing, \indexit{81}
  Todd-Coxeter Procedure, \indexit{551}
  `Trace', 225
    \sub for field elements, 579
    \sub of a matrix, 225
  `TracedCosetFpGroup', 465
  `TraceImmediateMethods', 79
  `TraceMat', 225
  `TraceMethods', 79
  `TracePolynomial', 578
  Tracing generator images through Tietze transformations, \indexit{495}
  Tracing Methods, \indexit{79}
  `TransferDiagram', 811
  `Transformation', 552
  `TransformationData', 552
  `TransformationFamily', 552
  `TransformationNC', 552
  `TransformationRelation', 554
  `TransformationType', 552
  `TransformingPermutations', 761
  `TransformingPermutationsCharacterTables', 761
  transitive, 404
  `TransitiveClosureBinaryRelation', 314
  `TransitiveGroup', 516
  `TransitiveIdentification', 516
  Transitive Permutation Groups, \indexit{516}
  transitive relation, 313
  `Transitivity', for characters, 776
    \sub for class functions, 776
    \sub for group actions, 404
  `TranslatorSubalgebra', 636
  transporter, 400
  `TransposedMat', 226
  `TransposedMatAttr', 226
  `TransposedMatDestructive', 227
  `TransposedMatImmutable', 226
  `TransposedMatMutable', 226
  `TransposedMatOp', 226
  `TransposedMatrixGroup', 427
  Transversals, \indexit{355}
  Triangular Matrices, \indexit{233}
  `TriangulizedIntegerMat', 240
  `TriangulizedIntegerMatTransform', 240
  `TriangulizedNullspaceMat', 228
  `TriangulizedNullspaceMatDestructive', 228
  `TriangulizeIntegerMat', 240
  `TriangulizeMat', 228
  `TrivialCharacter', 772
  `TrivialGroup', 508
  `TrivialIterator', 277
  `TrivialSubalgebra', 618
  `TrivialSubgroup', 360
  `TrivialSubmagmaWithOne', 322
  `TrivialSubmodule', 572
  `TrivialSubmonoid', 543
  `TrivialSubnearAdditiveMagmaWithZero', 557
  `TrivialSubspace', 597
  `TryCosetTableInWholeGroup', 468
  `TryGcdCancelExtRepPolynomials', 688
  `Tuples', 151
  tuple stabilizer, 399
  `TwoClosure', 424
  `TwoCoboundaries', 456
  `TwoCocycles', 456
  `TwoCohomology', 456
  `TwoGroup' library, 518
  `TwoSidedIdeal', 561
  `TwoSidedIdealByGenerators', 562
  `TwoSidedIdealNC', 562
  `TwoSquares', 144
  type, boolean, 169
    \sub cyclotomic, 157
    \sub records, 259
    \sub strings, 248
  `TypeObj', 125
  `TypeOfDefaultGeneralMapping', 311
  Types, \indexit{125}
  `TzEliminate', 490
  `TzFindCyclicJoins', 491
  `TzGo', 488
  `TzGoGo', 489
  `TzImagesOldGens', 496
  `TzInitGeneratorImages', 495
  `TzNewGenerator', 487
  `TzOptions', 500
  `TzPreImagesNewGens', 496
  `TzPrint', 486
  `TzPrintGeneratorImages', 496
  `TzPrintGenerators', 485
  `TzPrintLengths', 486
  `TzPrintOptions', 501
  `TzPrintPairs', 486
  `TzPrintPresentation', 486
  `TzPrintRelators', 485
  `TzPrintStatus', 486
  `TzSearch', 490
  `TzSearchEqual', 491
  `TzSort', 479
  `TzSubstitute', 492
  `TzSubstituteCyclicJoins', 495
\letter U
  $u_N$, 162
  `UglyVector', 610
  `Unbind', 44
    \sub for lists, 178
  `UnbindGlobal', 45
  `UnderlyingCharacteristic', 735
  `UnderlyingCharacterTable', 766
  `UnderlyingElement', fp group elements, 463
    \sub fp semigroup elements, 549
  `Underlying\-Element\-Of\-Rees\-Matrix\-Semigroup\-Element', 542
  `Underlying\-Element\-Of\-Rees\-Zero\-Matrix\-Semigroup\-Element', 542
  `UnderlyingExternalSet', 408
  `UnderlyingFamily', 638
  `UnderlyingGeneralMapping', 304
  `UnderlyingGroup', for character tables, 728
    \sub for tables of marks, 707
  `UnderlyingLeftModule', 600
  `UnderlyingLieAlgebra', 644
  `UnderlyingMagma', 661
  `UnderlyingRelation', 304
  `UnInstallCharReadHookFunc', 107
  `Union', 273
  union, of collections, 273
    \sub of sets, 196
  `Union2', 273
  `UnionBlist', 210
  `Unique', 198
  `UniteBlist', 211
  `UniteBlistList', 211
  `UniteSet', 196
  `Units', 565
  Units and Factorizations, \indexit{565}
  `UnivariatenessTestRationalFunction', 672
  `UnivariatePolynomial', 671
  `UnivariatePolynomialByCoefficients', 671
  `UnivariatePolynomialRing', 680
  Univariate Polynomial Rings, \indexit{680}
  Univariate Polynomials, \indexit{671}
  `Univariate\-Rational\-Function\-By\-Coefficients', 677
  Univariate Rational Functions, \indexit{677}
  `UniversalEnvelopingAlgebra', 650
  Universal Enveloping Algebras, \indexit{650}
  UNIX, features, 27
    \sub options, 27
  `UNIXSelect', 98
  `Unknown', 167
  `UnloadSmallGroupsData', 519
  `UnorderedTuples', 150
  Unpacking, \indexit{828}
  `UnprofileFunctions', 83
  `UnprofileMethods', 83
  `until', 52
  `UntraceMethods', 79
  `UpdateMap', 809
  `UpEnv', 71
  `UpperCentralSeriesOfGroup', 369
  `UpperSubdiagonal', 233
  `UseBasis', 574
  `UseFactorRelation', 295
  Useful Categories for all Elements of a Family, \indexit{299}
  Useful Categories of Elements, \indexit{297}
  `UseIsomorphismRelation', 295
  User Streams, \indexit{104}
  `UseSubsetRelation', 295
  utilities for editing GAP files, 75
\letter V
  $v_N$, 162
  `Valuation', 691
  `Value', 674
  `ValueCochain', 653
  `ValueGlobal', 45
  `ValueMolienSeries', 789
  `ValueOption', 89
  `ValuePol', 219
  `ValuesOfClassFunction', 766
  Variable Access in a Break Loop, \indexit{71}
  Variables, \indexit{43}
  Vectors as coefficients of polynomials, \indexit{218}
  `VectorSpace', 596
  `Vector\-Space\-By\-Pcgs\-Of\-Elementary\-Abelian\-Group', 447
  Vector Space Homomorphisms, \indexit{607}
  Vector Spaces Handled By Nice Bases, \indexit{609}
  `vi', 75
  `View', 66
  View and Print, \indexit{66}
  `ViewObj', 67
    \sub for character tables, 744
    \sub for class functions, 770
    \sub for tables of marks, 703
  `vim', 75
  `VirtualCharacter', 771
  virtual character, 773
  virtual characters, 764
\letter W
  $w_N$, 162
  `WedgeGModule ', 694
  `WeekDay', 257
  `WeightLexOrdering', 281
  `WeightOfGenerators', 282
  `WeightsTom', 709
  `WeightVecFFE', 218
  `WeylGroup', 646
  `WeylOrbitIterator', 647
  `Where', 70
  While, \indexit{52}
  `while' loop, 52
  Whitespaces, \indexit{41}
  Why Class Functions?, \indexit{764}
  `WordAlp', 253
  words, in generators, 351
  Working with large degree permutation groups, \indexit{425}
  `WreathProduct', 505
  wreath product embedding, 506
  `WreathProductImprimitiveAction', 506
  `WreathProductOrdering', 283
  `WreathProductProductAction', 506
  Wreath Products, \indexit{505}
  `WriteAll', 101
  `WriteByte', 101
  `WriteLine', 101
\letter X
  $x_N$, 162
\letter Y
  $y_N$, 162
\letter Z
  `Z', 581
  `ZClassRepsQClass', 431
  `Zero', 291
  `ZeroAttr', 291
  `ZeroCoefficient', 662
  `ZeroCoefficientRatFun', 686
  `ZeroImmutable', 291
  `ZeroMapping', 303
  `ZeroMutable', 291
  `ZeroOp', 291
  `ZeroSameMutability', 291
  `ZeroSM', 291
  `ZippedProduct', 688
  `ZippedSum', 688
  `ZmodnZ', 135
  `ZmodnZObj', 135
  `ZmodpZ', 135
  `ZmodpZNC', 135
  `ZumbroichBase', 592
  `Zuppos', 374
