\indexentry{InfoXMod@\texttt{InfoXMod}|hyperpage}{6} \indexentry{crossed module|hyperpage}{7} \indexentry{2d-object|hyperpage}{7} \indexentry{XMod@\texttt {XMod}|hyperpage}{7} \indexentry{XModByBoundaryAndAction@\texttt {XModByBoundaryAndAction}|hyperpage}{7} \indexentry{XModByTrivialAction@\texttt {XModByTrivialAction}|hyperpage}{7} \indexentry{XModByNormalSubgroup@\texttt {XModByNormalSubgroup}|hyperpage}{7} \indexentry{XModByCentralExtension@\texttt {XModByCentralExtension}|hyperpage}{7} \indexentry{XModByAutomorphismGroup@\texttt {XModByAutomorphismGroup}|hyperpage}{7} \indexentry{XModByInnerAutomorphismGroup@\texttt {XModByInnerAutomorphismGroup}|hyperpage}{7} \indexentry{XModByGroupOfAutomorphisms@\texttt {XModByGroupOfAutomorphisms}|hyperpage}{7} \indexentry{XModByAbelianModule@\texttt {XModByAbelianModule}|hyperpage}{7} \indexentry{DirectProduct@\texttt {DirectProduct}|hyperpage}{7} \indexentry{Source@\texttt {Source}|hyperpage}{8} \indexentry{Range@\texttt {Range}|hyperpage}{8} \indexentry{Boundary@\texttt {Boundary}|hyperpage}{8} \indexentry{AutoGroup@\texttt {AutoGroup}|hyperpage}{8} \indexentry{XModAction@\texttt {XModAction}|hyperpage}{8} \indexentry{Size@\texttt {Size}|hyperpage}{8} \indexentry{Name@\texttt {Name}|hyperpage}{8} \indexentry{display a 2d-object|hyperpage}{8} \indexentry{SubXMod@\texttt {SubXMod}|hyperpage}{9} \indexentry{IdentitySubXMod@\texttt {IdentitySubXMod}|hyperpage}{9} \indexentry{NormalSubXMods@\texttt {NormalSubXMods}|hyperpage}{9} \indexentry{pre-crossed module|hyperpage}{9} \indexentry{PreXModByBoundaryAndAction@\texttt {PreXModByBoundaryAndAction}|hyperpage}{9} \indexentry{SubPreXMod@\texttt {SubPreXMod}|hyperpage}{9} \indexentry{Peiffer subgroup|hyperpage}{10} \indexentry{PeifferSubgroup@\texttt {PeifferSubgroup}|hyperpage}{10} \indexentry{XModByPeifferQuotient@\texttt {XModByPeifferQuotient}|hyperpage}{10} \indexentry{IsPermXMod@\texttt {IsPermXMod}|hyperpage}{10} \indexentry{IsPcPreXMod@\texttt {IsPcPreXMod}|hyperpage}{10} \indexentry{cat1-group|hyperpage}{10} \indexentry{Source@\texttt {Source}|hyperpage}{10} \indexentry{Range@\texttt {Range}|hyperpage}{10} \indexentry{TailMap@\texttt {TailMap}|hyperpage}{11} \indexentry{HeadMap@\texttt {HeadMap}|hyperpage}{11} \indexentry{RangeEmbedding@\texttt {RangeEmbedding}|hyperpage}{11} \indexentry{KernelEmbedding@\texttt {KernelEmbedding}|hyperpage}{11} \indexentry{Boundary@\texttt {Boundary}|hyperpage}{11} \indexentry{Name@\texttt {Name}|hyperpage}{11} \indexentry{Size@\texttt {Size}|hyperpage}{11} \indexentry{Cat1@\texttt {Cat1}|hyperpage}{11} \indexentry{PreCat1ByTailHeadEmbedding@\texttt {PreCat1ByTailHeadEmbedding}|hyperpage}{11} \indexentry{PreCat1ByEndomorphisms@\texttt {PreCat1ByEndomorphisms}|hyperpage}{11} \indexentry{PreCat1ByNormalSubgroup@\texttt {PreCat1ByNormalSubgroup}|hyperpage}{11} \indexentry{Cat1ByPeifferQuotient@\texttt {Cat1ByPeifferQuotient}|hyperpage}{11} \indexentry{Reverse@\texttt {Reverse}|hyperpage}{11} \indexentry{Cat1OfXMod@\texttt {Cat1OfXMod}|hyperpage}{12} \indexentry{XModOfCat1@\texttt {XModOfCat1}|hyperpage}{12} \indexentry{PreCat1OfPreXMod@\texttt {PreCat1OfPreXMod}|hyperpage}{12} \indexentry{PreXModOfPreCat1@\texttt {PreXModOfPreCat1}|hyperpage}{12} \indexentry{selection of a small cat1-group|hyperpage}{13} \indexentry{Cat1Select@\texttt {Cat1Select}|hyperpage}{13} \indexentry{2d-mapping|hyperpage}{15} \indexentry{morphism of 2d-object|hyperpage}{15} \indexentry{crossed module morphism|hyperpage}{15} \indexentry{Source@\texttt {Source}|hyperpage}{15} \indexentry{Range@\texttt {Range}|hyperpage}{15} \indexentry{SourceHom@\texttt {SourceHom}|hyperpage}{15} \indexentry{RangeHom@\texttt {RangeHom}|hyperpage}{15} \indexentry{morphism|hyperpage}{15} \indexentry{IsXModMorphism@\texttt {IsXModMorphism}|hyperpage}{15} \indexentry{IsCat1Morphism@\texttt {IsCat1Morphism}|hyperpage}{15} \indexentry{IsPreXModMorphism@\texttt {IsPreXModMorphism}|hyperpage}{15} \indexentry{IsPreCat1Morphism@\texttt {IsPreCat1Morphism}|hyperpage}{15} \indexentry{IsInjective@\texttt {IsInjective}|hyperpage}{16} \indexentry{IsSurjective@\texttt {IsSurjective}|hyperpage}{16} \indexentry{IsSingleValued@\texttt {IsSingleValued}|hyperpage}{16} \indexentry{IsTotal@\texttt {IsTotal}|hyperpage}{16} \indexentry{IsBijective@\texttt {IsBijective}|hyperpage}{16} \indexentry{IsEndomorphism2dObject@\texttt {IsEndomorphism2dObject}|hyperpage}{16} \indexentry{IsAutomorphism2dObject@\texttt {IsAutomorphism2dObject}|hyperpage}{16} \indexentry{XModMorphism@\texttt {XModMorphism}|hyperpage}{16} \indexentry{XModMorphismByHoms@\texttt {XModMorphismByHoms}|hyperpage}{16} \indexentry{PreXModMorphism@\texttt {PreXModMorphism}|hyperpage}{16} \indexentry{PreXModMorphismByHoms@\texttt {PreXModMorphismByHoms}|hyperpage}{16} \indexentry{InclusionMorphism2dObjects@\texttt {InclusionMorphism2dObjects}|hyperpage}{16} \indexentry{InnerAutomorphismXMod@\texttt {InnerAutomorphismXMod}|hyperpage}{16} \indexentry{IdentityMapping@\texttt {IdentityMapping}|hyperpage}{16} \indexentry{IsomorphismPermObject@\texttt {IsomorphismPermObject}|hyperpage}{16} \indexentry{display a 2d-mapping|hyperpage}{16} \indexentry{Cat1Morphism@\texttt {Cat1Morphism}|hyperpage}{17} \indexentry{Cat1MorphismByHoms@\texttt {Cat1MorphismByHoms}|hyperpage}{17} \indexentry{PreCat1Morphism@\texttt {PreCat1Morphism}|hyperpage}{17} \indexentry{PreCat1MorphismByHoms@\texttt {PreCat1MorphismByHoms}|hyperpage}{17} \indexentry{InclusionMorphism2dObjects@\texttt {InclusionMorphism2dObjects}|hyperpage}{17} \indexentry{InnerAutomorphismCat1@\texttt {InnerAutomorphismCat1}|hyperpage}{17} \indexentry{IdentityMapping@\texttt {IdentityMapping}|hyperpage}{17} \indexentry{IsmorphismPermObject@\texttt {IsmorphismPermObject}|hyperpage}{17} \indexentry{SmallerDegreePerm2dObject@\texttt {SmallerDegreePerm2dObject}|hyperpage}{17} \indexentry{operations on morphisms|hyperpage}{18} \indexentry{Order@\texttt {Order}|hyperpage}{18} \indexentry{CompositionMorphism@\texttt {CompositionMorphism}|hyperpage}{18} \indexentry{Kernel@\texttt {Kernel}|hyperpage}{18} \indexentry{Kernel2dMapping@\texttt {Kernel2dMapping}|hyperpage}{18} \indexentry{up 2d-mapping of 2d-object|hyperpage}{20} \indexentry{Whitehead multiplication|hyperpage}{20} \indexentry{IsDerivation@\texttt {IsDerivation}|hyperpage}{20} \indexentry{IsSection@\texttt {IsSection}|hyperpage}{20} \indexentry{IsUp2dMapping@\texttt {IsUp2dMapping}|hyperpage}{20} \indexentry{derivation, of crossed module|hyperpage}{20} \indexentry{Whitehead monoid|hyperpage}{20} \indexentry{regular derivation|hyperpage}{20} \indexentry{Whitehead group|hyperpage}{20} \indexentry{section, of cat1-group|hyperpage}{20} \indexentry{Whitehead multiplication|hyperpage}{20} \indexentry{DerivationByImages@\texttt {DerivationByImages}|hyperpage}{20} \indexentry{Object2d@\texttt {Object2d}|hyperpage}{20} \indexentry{GeneratorImages@\texttt {GeneratorImages}|hyperpage}{21} \indexentry{SectionByImages@\texttt {SectionByImages}|hyperpage}{21} \indexentry{SectionByDerivation@\texttt {SectionByDerivation}|hyperpage}{21} \indexentry{DerivationBySection@\texttt {DerivationBySection}|hyperpage}{21} \indexentry{RegularDerivations@\texttt {RegularDerivations}|hyperpage}{22} \indexentry{AllDerivations@\texttt {AllDerivations}|hyperpage}{22} \indexentry{RegularSections@\texttt {RegularSections}|hyperpage}{22} \indexentry{AllSections@\texttt {AllSections}|hyperpage}{22} \indexentry{ImagesList@\texttt {ImagesList}|hyperpage}{22} \indexentry{ImagesTable@\texttt {ImagesTable}|hyperpage}{22} \indexentry{CompositeDerivation@\texttt {CompositeDerivation}|hyperpage}{23} \indexentry{ImagePositions@\texttt {ImagePositions}|hyperpage}{23} \indexentry{CompositeSection@\texttt {CompositeSection}|hyperpage}{23} \indexentry{WhiteheadGroupTable@\texttt {WhiteheadGroupTable}|hyperpage}{23} \indexentry{WhiteheadMonoidTable@\texttt {WhiteheadMonoidTable}|hyperpage}{23} \indexentry{WhiteheadPermGroup@\texttt {WhiteheadPermGroup}|hyperpage}{23} \indexentry{WhiteheadTransMonoid@\texttt {WhiteheadTransMonoid}|hyperpage}{23} \indexentry{actor|hyperpage}{25} \indexentry{WhiteheadXMod@\texttt {WhiteheadXMod}|hyperpage}{25} \indexentry{LueXMod@\texttt {LueXMod}|hyperpage}{25} \indexentry{NorrieXMod@\texttt {NorrieXMod}|hyperpage}{25} \indexentry{ActorXMod@\texttt {ActorXMod}|hyperpage}{25} \indexentry{AutomorphismPermGroup@\texttt {AutomorphismPermGroup}|hyperpage}{25} \indexentry{crossed square|hyperpage}{25} \indexentry{Centre@\texttt {Centre}|hyperpage}{25} \indexentry{InnerActor@\texttt {InnerActor}|hyperpage}{25} \indexentry{InnerMorphism@\texttt {InnerMorphism}|hyperpage}{25} \indexentry{induced crossed module|hyperpage}{28} \indexentry{InducedXMod@\texttt {InducedXMod}|hyperpage}{28} \indexentry{InducedCat1@\texttt {InducedCat1}|hyperpage}{28} \indexentry{IsInducedXMod@\texttt {IsInducedXMod}|hyperpage}{28} \indexentry{IsInducedCat1@\texttt {IsInducedCat1}|hyperpage}{28} \indexentry{MorphismOfInducedXMod@\texttt {MorphismOfInducedXMod}|hyperpage}{28} \indexentry{AllInducedXMods@\texttt {AllInducedXMods}|hyperpage}{30} \indexentry{crossed module|hyperpage}{31} \indexentry{cat2-group|hyperpage}{31} \indexentry{3d-object|hyperpage}{31} \indexentry{crossed pairing|hyperpage}{31} \indexentry{XSq@\texttt {XSq}|hyperpage}{32} \indexentry{XSqByNormalSubgroups@\texttt {XSqByNormalSubgroups}|hyperpage}{32} \indexentry{ActorXSq@\texttt {ActorXSq}|hyperpage}{32} \indexentry{Transpose3dObject@\texttt {Transpose3dObject}|hyperpage}{32} \indexentry{Name@\texttt {Name}|hyperpage}{32} \indexentry{IsXSq@\texttt {IsXSq}|hyperpage}{33} \indexentry{Is3dObject@\texttt {Is3dObject}|hyperpage}{33} \indexentry{IsPerm3dObject@\texttt {IsPerm3dObject}|hyperpage}{33} \indexentry{IsPc3dObject@\texttt {IsPc3dObject}|hyperpage}{33} \indexentry{IsFp3dObject@\texttt {IsFp3dObject}|hyperpage}{33} \indexentry{IsPreXSq@\texttt {IsPreXSq}|hyperpage}{33} \indexentry{Up2dObject@\texttt {Up2dObject}|hyperpage}{34} \indexentry{Left2dObject@\texttt {Left2dObject}|hyperpage}{34} \indexentry{Down2dObject@\texttt {Down2dObject}|hyperpage}{34} \indexentry{Right2dObject@\texttt {Right2dObject}|hyperpage}{34} \indexentry{DiagonalAction@\texttt {DiagonalAction}|hyperpage}{34} \indexentry{XPair@\texttt {XPair}|hyperpage}{34} \indexentry{ImageElmXPair@\texttt {ImageElmXPair}|hyperpage}{34} \indexentry{morphism of 3d-object|hyperpage}{34} \indexentry{crossed square morphism|hyperpage}{34} \indexentry{3d-mapping|hyperpage}{34} \indexentry{Source@\texttt {Source}|hyperpage}{34} \indexentry{Range@\texttt {Range}|hyperpage}{34} \indexentry{Up2dMorphism@\texttt {Up2dMorphism}|hyperpage}{34} \indexentry{Left2dMorphism@\texttt {Left2dMorphism}|hyperpage}{34} \indexentry{Down2dMorphism@\texttt {Down2dMorphism}|hyperpage}{34} \indexentry{Right2dMorphism@\texttt {Right2dMorphism}|hyperpage}{34} \indexentry{IsXSqMorphism@\texttt {IsXSqMorphism}|hyperpage}{35} \indexentry{IsPreXSqMorphism@\texttt {IsPreXSqMorphism}|hyperpage}{35} \indexentry{IsBijective@\texttt {IsBijective}|hyperpage}{35} \indexentry{IsAutomorphism3dObject@\texttt {IsAutomorphism3dObject}|hyperpage}{35} \indexentry{inclusion mapping|hyperpage}{36} \indexentry{restriction mapping|hyperpage}{36} \indexentry{InclusionMappingGroups@\texttt {InclusionMappingGroups}|hyperpage}{36} \indexentry{RestrictionMappingGroups@\texttt {RestrictionMappingGroups}|hyperpage}{36} \indexentry{MappingToOne@\texttt {MappingToOne}|hyperpage}{36} \indexentry{endomorphism classes|hyperpage}{37} \indexentry{EndomorphismClasses@\texttt {EndomorphismClasses}|hyperpage}{37} \indexentry{EndoClassNaturalHom@\texttt {EndoClassNaturalHom}|hyperpage}{37} \indexentry{EndoClassIsomorphism@\texttt {EndoClassIsomorphism}|hyperpage}{37} \indexentry{EndoClassConjugators@\texttt {EndoClassConjugators}|hyperpage}{37} \indexentry{AutoGroup@\texttt {AutoGroup}|hyperpage}{37} \indexentry{InnerAutomorphismByNormalSubgroup@\texttt {InnerAutomorphismByNormalSubgroup}|hyperpage}{38} \indexentry{IsGroupOfAutomorphisms@\texttt {IsGroupOfAutomorphisms}|hyperpage}{38} \indexentry{abelian module|hyperpage}{38} \indexentry{AbelianModuleObject@\texttt {AbelianModuleObject}|hyperpage}{38} \indexentry{IsAbelianModule@\texttt {IsAbelianModule}|hyperpage}{38} \indexentry{AbelianModuleGroup@\texttt {AbelianModuleGroup}|hyperpage}{38} \indexentry{AbelianModuleAction@\texttt {AbelianModuleAction}|hyperpage}{38} \indexentry{distinct and common representatives|hyperpage}{39} \indexentry{DistinctRepresentatives@\texttt {DistinctRepresentatives}|hyperpage}{39} \indexentry{CommonRepresentatives@\texttt {CommonRepresentatives}|hyperpage}{39} \indexentry{CommonTransversal@\texttt {CommonTransversal}|hyperpage}{39} \indexentry{IsCommonTransversal@\texttt {IsCommonTransversal}|hyperpage}{39} \indexentry{version 1 for \textsf{GAP} 3|hyperpage}{40} \indexentry{version 2.001 for \textsf{GAP} 4|hyperpage}{40}