GAP (XMod) - Index

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### Index

2d-domain 2.
2d-group 2.
2d-mapping 3.
2dimensional-domain with objects 10.1
3d-domain 8.
3d-group 8.
3d-mapping 8.3
4d-domain 9.
4d-group 9.
abelian module 13.2
`AbelianModuleAction` 13.2-1
`AbelianModuleGroup` 13.2-1
`AbelianModuleObject` 13.2-1
actor 6.1
`ActorCrossedSquare` 8.2-4
`ActorXMod` 6.1-2
`AllCat1Groups` 2.6-3
`AllCat1GroupsIterator` 2.6-3
`AllCat1GroupsMatrix` 2.6-2 2.6-3
`AllCat1GroupsUpToIsomorphism` 2.6-3
`AllCat1GroupsWithImage` 2.6-1
`AllCat1GroupsWithImageIterator` 2.6-1
`AllCat1GroupsWithImageNumber` 2.6-1
`AllCat1GroupsWithImageUpToIsomorphism` 2.6-1
`AllCat2GroupFamilies` 8.5-4
`AllCat2Groups` 8.5-4
`AllCat2GroupsIterator` 8.5-4
`AllCat2GroupsMatrix` 8.5-3 8.5-4
`AllCat2GroupsUpToIsomorphism` 8.5-4
`AllCat2GroupsWithFixedUp` 8.5-2
`AllCat2GroupsWithFixedUpAndLeftRange` 8.5-2
`AllCat2GroupsWithImages` 8.5-1
`AllCat2GroupsWithImagesIterator` 8.5-1
`AllCat2GroupsWithImagesNumber` 8.5-1
`AllCat2GroupsWithImagesUpToIsomorphism` 8.5-1
`AllCat3Groups` 9.2-1
`AllCat3GroupsNumber` 9.2-1
`AllCat3GroupTriples` 9.2-1
`AllDerivations` 5.2-1
`AllInducedXMods` 7.2-2
`AllLoopsXMod` 11.1-1
`AllSections` 5.2-4
`AllStemGroupFamilies` 4.2-2
`AllStemGroupIds` 4.2-2
`AllXMods` 4.1-12
`AllXModsUpToIsomorphism` 4.1-12
`AllXModsWithGroups` 4.1-12
`AreIsoclinicDomains`, for crossed modules of groups 4.3-1
for groups 4.2-1
AutoGroup 2.1-9
`AutomorphismPermGroup` 6.1-1
`Back3DimensionalGroup` 9.1-2
`Boundary`, for cat1-groups 2.4-2
for crossed modules 2.1-9
CAT1_LIST_MAX_SIZE 2.7
CAT1_LIST_NUMBERS 2.7
`Cat1Group` 2.4-1
`Cat1GroupByPeifferQuotient` 2.4-5
`Cat1GroupMorphism` 3.3-1
`Cat1GroupMorphismByGroupHomomorphisms` 3.3-1
`Cat1GroupMorphismOfXModMorphism` 3.3-2
`Cat1GroupOfXMod` 2.5-3
`Cat1GroupToHAP` 12.1-2
`Cat1Select` 2.7-1
`Cat2Group` 8.4-1
`Cat2GroupMorphism` 8.4-5
`Cat2GroupMorphismByCat1GroupMorphisms` 8.4-5
`Cat2GroupMorphismByGroupHomomorphisms` 8.4-5
`Cat2GroupOfCrossedSquare` 8.4-6
`Cat3Group` 9.1-1
cat\(^1\)-group 2.4
cat\(^2\)-group 8.4
cat\(^3\)-group 9.
cat\(^n\)-group 9.3
`CatnGroup` 9.3-1
`CatnGroupLists`, for cat1-groups 2.6-4
for cat2-groups 8.5-4
`CatnGroupNumbers`, for cat1-groups 2.6-4
for cat2-groups 8.5-4
`CatOneGroupToXMod` 12.1-2
`Centralizer` 4.1-7
`CentralQuotient` 4.1-8
for crossed modules 8.2-10
`CentreXMod` 4.1-7
`CommutatorSubXMod` 4.1-4
`CompositionMorphism` 3.4-1
`CoproductInfo` 7.1-1
`CoproductXMod` 7.1-1
`CrossActionSubgroup` 4.1-4
crossed module 2.1
crossed module morphism 3.1
crossed module of groupoids 10.
crossed module over a groupoid 10.1
crossed pairing 8.1
crossed square 6.1-2 8.1
crossed square morphism 8.3
`CrossedPairing` 8.2-14
`CrossedPairingByCommutators` 8.2-2
`CrossedPairingByConjugators` 8.2-5
`CrossedPairingByDerivations` 8.2-4
`CrossedPairingByPreImages` 8.2-7
`CrossedPairingBySingleXModAction` 8.2-3
`CrossedPairingMap` 8.2-14
`CrossedSquare` 8.2-8
`CrossedSquareByAutomorphismGroup` 8.2-5
`CrossedSquareByNormalSubgroups` 8.2-2
`CrossedSquareByNormalSubXMod` 8.2-3
`CrossedSquareByPullback` 8.2-6
`CrossedSquareByXMods` 8.2-1
`CrossedSquareByXModSplitting` 8.2-7
`CrossedSquareMorphism` 8.3-1
`CrossedSquareMorphismByGroupHomomorphisms` 8.3-1
`CrossedSquareMorphismByXModMorphisms` 8.3-1
`CrossedSquareOfCat2Group` 8.4-6
derivation, of crossed module 5.1
`DerivationByImages` 5.1-1
`DerivationBySection` 5.1-3
`DerivationClass` 5.2-1
`DerivedSubXMod` 4.1-5
`Diagonal2DimensionalGroup` 8.2-12
`DiagonalAction` 8.2-12
`DiagonalCat1Group` 2.4-3
`DirectProduct` 8.4-2
for cat1-groups 2.4-7
for crossed modules 2.1-8
`Displacement` 4.1-3
`DisplacementGroup` 4.1-3
`DisplacementSubgroup` 4.1-3
display a 2d-mapping 3.2-3
Display for a 2d-group 2.1-11
Display for a 3d-group 8.2-1
`DisplayLeadMaps` 8.4-3
`Down2DimensionalGroup` 8.2-12
`Down2DimensionalMorphism` 8.3-2
`Down3DimensionalGroup` 9.1-2
`ExternalSetXMod` 2.1-11
`FactorPreXMod` 4.1-1
`FixedPointSubgroupXMod` 4.1-6
free loop space 11.1
`Front3DimensionalGroup` 9.1-2
`GeneratingAutomorphisms` 6.1-1
`GroupGroupoid` 2.9-1
`GroupGroupoidElement` 2.9-2
`HeadMap` 2.4-2
`IdCat1Group` 12.1-3
`IdentityDerivation` 5.1-4
`IdentityMapping`, for pre-xmods 3.2-3
for precat1-morphisms 3.3-1
`IdentitySection` 5.1-4
`IdGroup`, for 2d-groups 2.8-1
for crossed modules 2.1-11
`ImageElmCrossedPairing` 8.2-14
`ImageElmXModAction` 2.1-10
`ImagesList` 5.2-2
`ImagesTable` 5.2-1
inclusion mapping 13.1
`InclusionMappingGroups` 13.1-1
`InclusionMorphism2DimensionalDomains`, for cat1-groups 3.3-1
for crossed modules 3.2-3
`InclusionMorphismHigherDimensionalDomains` 8.3-4
induced cat1-groups 7.3
induced crossed module 7.2
`InducedCat1Group` 7.3-1
`InducedCat1GroupByFreeProduct` 7.3-1
`InducedXMod` 7.2-1
`InducedXModByCopower` 7.2-1
`InducedXModBySurjection` 7.2-1
`InfoXMod` 1.
`InitCatnGroupRecords` 2.6-4
`InnerActorXMod` 6.1-3
`InnerAutomorphismCat1` 3.3-1
`InnerAutomorphismsByNormalSubgroup` 13.1-2
`InnerAutomorphismXMod` 3.2-3
`InnerMorphism` 6.1-3
`IntersectionSubXMods` 4.1-2
Is2DimensionalDomain 2.2
Is2DimensionalGroup 2.2
Is2DimensionalGroupWithObjects 10.1-2
`Is3dObject` 8.2-11
`IsAbelian2DimensionalGroup` 4.1-9
`IsAbelian3DimensionalGroup` 8.2-13
`IsAbelianModule` 13.2-1
IsAbelianModule2DimensionalGroup 2.2
`IsAspherical2DimensionalGroup` 4.1-9
`IsAutomorphism3dObject` 8.3-3
IsAutomorphismGroup2DimensionalGroup 2.2
`IsAutomorphismGroup3DimensionalGroup` 8.2-13
`IsBijective` 8.3-3
for pre-xmod morphisms 3.2-2
`IsCat1Group` 2.5-1
`IsCat1GroupMorphism` 3.3-1
`IsCat2Group` 8.4-1
`IsCat3Group` 9.1-1
IsCentralExtension2DimensionalGroup 2.2
`IsCentralExtension3DimensionalGroup` 8.2-13
`IsCrossedSquare` 8.2-11
`IsCrossedSquareMorphism` 8.3-3
`IsDerivation` 5.1-1
`IsDirectProductWithCompleteDigraphDomain` 10.1-2
`IsEndo2DimensionalMapping` 3.2-2
`IsEndomorphism3dObject` 8.3-3
`IsFaithful2DimensionalGroup` 4.1-9
`IsFp2DimensionalGroup` 2.2-1
`IsFp3dObject` 8.2-11
`IsFpPreXModWithObjects` 10.1-3
`IsGroupOfAutomorphisms` 13.1-3
`IsIdentityCat1Group` 2.5-1
`IsInducedXMod` 7.2-1
`IsInjective`, for pre-xmod morphisms 3.2-2
IsMonoidOfUp2DimensionalMappingsObj 5.2
`IsNilpotent2DimensionalGroup` 4.1-10
IsNormal for crossed modules 2.2-1
`IsNormalSub3DimensionalGroup` 8.2-13
IsNormalSubgroup2DimensionalGroup 2.2
`IsoclinicMiddleLength`, for crossed modules of groups 4.3-3
for groups 4.2-3
`IsoclinicRank`, for crossed modules of groups 4.3-3
for groups 4.2-3
`IsoclinicStemDomain`, for crossed modules of groups 4.3-2
for groups 4.2-2
`Isoclinism`, for crossed modules 4.3-1
for groups 4.2-1
`IsomorphicPreCat1GroupWithIdentityEmbedding` 2.5-2
`IsomorphismByIsomorphisms` 3.2-4
`IsomorphismClassRepresentatives2dGroups` 4.1-12
`IsomorphismFp2DimensionalGroup`, for pre-cat1 morphisms 3.3-3
`IsomorphismPc2DimensionalGroup`, for pre-cat1 morphisms 3.3-3
for pre-xmod morphisms 3.2-4
`IsomorphismPerm2DimensionalGroup`, for pre-cat1 morphisms 3.3-3
for pre-xmod morphisms 3.2-4
`IsomorphismPermObject` 3.3-3
`IsomorphismToPreCat1GroupWithIdentityEmbedding` 2.5-2
`IsomorphismXMods` 4.1-11
`IsPc2DimensionalGroup` 2.2-1
`IsPc3dObject` 8.2-11
`IsPcPreXModWithObjects` 10.1-3
`IsPerm2DimensionalGroup` 2.2-1
`IsPerm3dObject` 8.2-11
`IsPermPreXModWithObjects` 10.1-3
`IsPreCat1GroupMorphism` 3.3-1
`IsPreCat1GroupWithIdentityEmbedding` 2.5-2
`IsPreCrossedSquare` 8.2-11
`IsPreCrossedSquareMorphism` 8.3-3
`IsPreXCat1Group` 2.5-1
`IsPreXMod` 2.2-1
`IsPreXModMorphism` 3.2-1
`IsPreXModWithObjects` 10.1-2
`IsSection` 5.1-3
`IsSimplyConnected2DimensionalGroup` 4.1-9
`IsSingleValued`, for pre-xmod morphisms 3.2-2
`IsStemDomain`, for crossed modules of groups 4.3-2
for groups 4.2-2
`IsSub2DimensionalGroup` 2.8-2
`IsSubCat1Group` 2.8-2
`IsSubPreCat1Group` 2.8-2
`IsSubPreXMod` 2.8-2
`IsSubXMod` 2.8-2
`IsSurjective`, for pre-xmod morphisms 3.2-2
`IsSymmetric3DimensionalGroup` 8.2-13
`IsTotal`, for pre-xmod morphisms 3.2-2
IsTrivialAction2DimensionalGroup 2.2
`IsTrivialAction3DimensionalGroup` 8.2-13
`IsUp2DimensionalMapping` 5.1-1
`IsXMod` 2.2-1
`IsXModMorphism` 3.2-1
`IsXModWithObjects` 10.1-2
`Kernel`, for 2d-mappings 3.4-2
`Kernel2DimensionalMapping` 3.4-2
`KernelCokernelXMod` 2.2-3
`KernelEmbedding` 2.4-2
`Left2DimensionalGroup` 8.2-12
`Left2DimensionalMorphism` 8.3-2
`Left3DimensionalGroup` 9.1-2
loop space 11.1
`LoopClasses` 11.1-1
`LoopsXMod` 11.1-1
`LowerCentralSeriesOfXMod` 4.1-10
`LueXMod` 6.1-2
`Mapping2ArgumentsByFunction` 8.2-14
`MappingToOne` 13.1-1
morphism 3.2
morphism of 2d-group 3.1
morphism of 3d-group 8.3
`MorphismOfInducedXMod` 7.2-1
`MorphismOfPullback`, for a crossed module by pullback 3.2-5
`Name` 8.2-12
for cat1-groups 2.4-2
for crossed modules 2.1-11
`NaturalMorphismByNormalSubPreXMod` 4.1-1
`NilpotencyClass2DimensionalGroup` 4.1-10
`Normalizer` 4.1-7
`NormalSubXMods` 2.2-2
`NorrieXMod` 6.1-2
ObjectList 10.1-4
operations on morphisms 3.4
order of a 2d-automorphism 3.2-3
Peiffer subgroup 2.3-1
`PeifferSubgroup` 2.3-2
`PermAutomorphismAsXModMorphism` 6.1-1
pre-crossed module 2.3
`PreCat1Group` 2.4-1
`PreCat1GroupByTailHeadEmbedding` 2.4-1
`PreCat1GroupMorphism` 3.3-1
`PreCat1GroupMorphismByGroupHomomorphisms` 3.3-1
`PreCat1GroupRecordOfPreXMod` 2.5-3
`PreCat1GroupWithIdentityEmbedding` 2.4-1
`PreCat2Group` 8.4-1
`PreCat2GroupByPreCat1Groups` 8.4-1
`PreCat2GroupMorphism` 8.4-5
`PreCat2GroupMorphismByGroupHomomorphisms` 8.4-5
`PreCat2GroupMorphismByPreCat1GroupMorphisms` 8.4-5
`PreCat3Group` 9.1-1
`PreCat3GroupByPreCat2Groups` 9.1-1
`PreCatnGroup` 9.3-1
`PreCrossedSquareByPreXMods` 8.2-1
`PreCrossedSquareMorphismByGroupHomomorphisms` 8.3-1
`PreCrossedSquareMorphismByPreXModMorphisms` 8.3-1
`PreXModByBoundaryAndAction` 2.3-1
`PreXModMorphism` 3.2-3
`PreXModMorphismByGroupHomomorphisms` 3.2-3
`PreXModRecordOfPreCat1Group` 2.5-3
`PrincipalDerivation` 5.1-2
`PrincipalDerivations` 5.2-3
`Range` 8.3-2
for 2d-group mappings 3.1-1
for cat1-groups 2.4-2
for crossed modules 2.1-9
`RangeEmbedding` 2.4-2
`RangeHom` 3.1-1
regular derivation 5.1
`RegularDerivations` 5.2-2
`RegularSections` 5.2-4
restriction mapping 13.1
`Right2DimensionalGroup` 8.2-12
`Right2DimensionalMorphism` 8.3-2
`Right3DimensionalGroup` 9.1-2
`Root2dGroup` 10.1-4
section, of cat1-group 5.1
`SectionByDerivation` 5.1-3
`SectionByHomomorphism` 5.1-3
selection of a small cat\(^1\)-group 2.7
`SinglePiecePreXModWithObjects` 10.1-1
`Size`, for cat1-groups 2.4-2
for crossed modules 2.1-11
`SmallCat1Group` 12.1-1
`SmallerDegreePermutationRepresentation2DimensionalGroup`, for perm 2d-groups 3.3-4
`Source` 8.3-2
for 2d-group mappings 3.1-1
for cat1-groups 2.4-2
for crossed modules 2.1-9
`SourceHom` 3.1-1
`StabilizerSubgroupXMod` 4.1-6
`StructureDescription`, for 2d-groups 2.8-1
`SubCat1Group` 2.4-6
`Subdiagonal2DimensionalGroup` 8.4-7
`SubPreCat1Group` 2.4-6
`SubPreXMod` 2.3-1
`SubXMod` 2.2-2
`TailMap` 2.4-2
`Transpose3DimensionalGroup`, for cat2-groups 8.4-4
for crossed squares 8.2-9
`TransposeCat1Group` 2.4-4
`TransposeIsomorphism` 2.4-4
`TrivialSubXMod` 2.2-2
up 2d-mapping of 2d-group 5.
`Up2DimensionalGroup` 8.2-12
`Up2DimensionalMorphism` 8.3-2
`Up3DimensionalGroup` 9.1-2
`UpGeneratorImages` 5.1-1
`UpImagePositions` 5.1-1
version 1 for GAP 3 14.1-1
version 2.001 for GAP 4 14.1-3
Whitehead group 5.1
Whitehead monoid 5.1
Whitehead multiplication 5.1
`WhiteheadGroupTable` 5.2-2
`WhiteheadMonoidTable` 5.2-1
`WhiteheadOrder` 5.1-5
`WhiteheadPermGroup` 5.2-2
`WhiteheadProduct` 5.1-5
`WhiteheadTransformationMonoid` 5.2-1
`WhiteheadXMod` 6.1-2
`XMod` 2.1-1
`XModAction`, for crossed modules of groupoids 10.1-4
for crossed modules of groups 2.1-9
`XModByAbelianModule` 2.1-7
`XModByAutomorphismGroup` 2.1-4
`XModByBoundaryAndAction` 2.1-1
`XModByCentralExtension` 2.1-5
`XModByGroupOfAutomorphisms` 2.1-4
`XModByInnerAutomorphismGroup` 2.1-4
`XModByNormalSubgroup` 2.1-2
`XModByPeifferQuotient` 2.3-2
`XModByPullback` 2.1-6
`XModByTrivialAction` 2.1-3
`XModCentre` 6.1-3
`XModMorphism` 3.2-3
`XModMorphismByGroupHomomorphisms` 3.2-3
`XModMorphismOfCat1GroupMorphism` 3.3-2
`XModOfCat1Group` 2.5-3

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