Creation of Automorphism Groups
AutomorphismGroup(G): Grp -> GrpAuto
Example GrpAuto_autogp-full (H67E1)
AutomorphismGroup(G, Q, I): Grp, SeqEnum[GrpElt], SeqEnum[SeqEnum[GrpElt]] -> GrpAuto
Access Functions
Group(A) : GrpAuto -> Grp
NumberOfGenerators(A) : GrpAuto -> RngIntElt
NumberOfPCGenerators(A) : GrpAuto -> RngIntElt
Generators(A) : GrpAuto -> SetEnum
PCGenerators(A) : GrpAuto -> SetIndx
InnerGenerators(A) : GrpAuto -> SeqEnum
CharacteristicSeries(A) : GrpAuto -> SeqEnum
IsSoluble(A) : GrpAuto -> BoolElt
IsSolubleAutomorphismGroupPGroup(A) : GrpAuto -> BoolElt
Order Functions
Order(A) : GrpAuto -> RngIntElt
FactoredOrder(A) : GrpAuto -> [ <RngIntElt, RngIntElt> ]
OuterOrder(A) : GrpAuto -> RngIntElt
Example GrpAuto_autogp-order (H67E2)
Representations of an Automorphism Group
PermutationRepresentation(A) : GrpAuto -> Map, GrpPerm, SetIndx
PermutationGroup(A) : GrpAuto -> GrpPerm
PermutationSupport(A) : GrpAuto -> SetIndx
PCGroupAutomorphismGroupPGroup(A) : GrpAuto -> BoolElt, Map, GrpPC
FPGroup(A) : GrpAuto -> GrpFP, Map
OuterFPGroup(A) : GrpAuto -> GrpFP, Map
Example GrpAuto_autogp-rep1 (H67E3)
Example GrpAuto_autogp-rep2 (H67E4)
Automorphisms
A . i : GrpAuto, RngIntElt -> GrpAutoElt
Identity(A) : GrpAuto -> GrpAutoElt
A ! f : GrpAuto, Map -> GrpAutoElt
Order(f) : GrpAutoElt -> RngIntElt
f * g : GrpAutoElt, GrpAutoElt -> GrpAutoElt
f ^ n : GrpAutoElt, RngIntElt -> GrpAutoElt
(g1, ..., gr) : GrpAutoElt, ..., GrpAutoElt -> GrpAutoElt
g eq h : GrpAutoElt, GrpAutoElt -> BoolElt
g ne h : GrpAutoElt, GrpAutoElt -> BoolElt
IsInner(f) : GrpAutoElt -> BoolElt, GrpElt
Example GrpAuto_autogp-elts (H67E5)
Example GrpAuto_characteristic-subgroups (H67E6)
Stored Attributes of an Automorphism Group
HasAttribute(A, s) : GrpAuto, MonStgElt -> BoolElt, .
Example GrpAuto_characteristicsubgps (H67E7)
Example GrpAuto_auto-maximals (H67E8)
Holomorphs
Holomorph(G) : Grp -> GrpPerm, HomGrp, HomGrp
Holomorph(G, A) : Grp, GrpAuto -> GrpPerm, HomGrp, HomGrp
Example GrpAuto_holomorph (H67E9)
Bibliography
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Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012