OnSubgroups(
subgroup,
aut ) F
For a group G and an automorphism aut of G,
OnSubgroups(
subgroup,
aut)
is the image of subgroup under aut
gap> G:=Group((1,2,3),(2,3)); Group([ (1,2,3), (2,3) ]) gap> alpha:=InnerAutomorphism(G,(1,2,3)); ^(1,2,3) gap> OnSubgroups(Subgroup(G,[(2,3)]),alpha); Group([ (1,3) ])
RepsCClassesGivenOrder(
group,
order ) O
RepsCClassesGivenOrder(
group,
order )
returns all elements of
order order up to conjugacy. Note that the representatives are not
always the smallest elements of each conjugacy class.
gap> RepsCClassesGivenOrder(SymmetricGroup(5),2); [ (4,5), (2,3)(4,5) ]
RDS manual