Access Functions

The functions described here provide access to basic information stored for an automorphism group \(A\).

Group(A): GrpAuto -> Grp

Given a group of automorphisms \(A\) of the group \(G\), return the base group \(G\) on which \(A\) acts.

NumberOfGenerators(A): GrpAuto -> RngIntElt

Ngens(A): GrpAuto -> RngIntElt

Given a group of automorphisms \(A\) of the group \(G\), return the number of defining generators for \(A\).

NumberOfPCGenerators(A): GrpAuto -> RngIntElt

NPCGenerators(A): GrpAuto -> RngIntElt

NPCgens(A): GrpAuto -> RngIntElt

Given a group of automorphisms \(A\) of the group \(G\), where a pc-representation has been created for \(A\) (and attribute PCGenerators is set on \(A\)), return the number of pc-generators for \(A\).

Generators(A): GrpAuto -> SetEnum

Given a group of automorphisms \(A\) of the group \(G\), return a set containing the defining generators of \(A\).

PCGenerators(A): GrpAuto -> SetIndx

Given a group of automorphisms \(A\) of the group \(G\), where a pc-representation has been created for \(A\) (and attribute PCGenerators is set on \(A\)), return an indexed set containing the pc-generators of \(A\).

InnerGenerators(A): GrpAuto -> SeqEnum

Given the full group of automorphisms \(A\) of the group \(G\), return a sequence of generators for the inner automorphism group of the base group of \(A\) (attribute InnerGenerators), if this attribute has been set.

CharacteristicSeries(A): GrpAuto -> SeqEnum

Given a group of automorphisms \(A\) of the group \(G\), return the value of the characteristic series of \(G\) used to compute \(A\), if this attribute has been set.

IsSoluble(A): GrpAuto -> BoolElt

IsSolvable(A): GrpAuto -> BoolElt

Given a group of automorphisms \(A\) of the group \(G\), return the value of \(A\)’s attribute Soluble, if this attribute has been set.

IsSolubleAutomorphismGroupPGroup(A): GrpAuto -> BoolElt

IsSolvableAutomorphismGroupPGroup(A): GrpAuto -> BoolElt

Given a group of automorphisms \(A\) of a \(p\)-group \(G\) constructed using the intrinsic AutomorphismGroup(G) or any equivalent alias, determine if \(A\) is soluble and return the result. This function also sets the Soluble attribute on \(A\).