[GAP Forum] How I can act an automorphism of a group to a quotient group

[Le Van Luyen]

Dear Masoud,

You could look the following GAP session:

gap> G:=DihedralGroup(32);
gap> H:=NormalSubgroups(G)[2];  ## H is a normal subgroup of G
gap> p:=NaturalHomomorphismByNormalSubgroup(G,H); ## p: G->G/H
gap> GH:=Range(p);  ## GH is the quotient G/H
gap> A:=AutomorphismGroup(G);  ## A=AutG
gap> a:=Random(A);  ## f is a element in AutG
gap> gH:=List(GH,x->PreImagesRepresentative(p,x));  ##gH is the list of
representatives {g_1,g_2,...,g_n}
gap> agH:=List(gH,x->x^a); ## agH:={g_1^a,g_2^a,...,g_n^a}
gap> aGH:=List(agH,x->x^p);

Then aGH is the list that you want to compute

Best regards,

Luyen