Dear Farzaneh,
You can restrict any group to its action on an orbit or set of orbits using the
operation Action.
For instance:
gap> g := AlternatingGroup(5);
Alt( [ 1 .. 5 ] )
gap> a := AutomorphismGroup(g);
<group of size 120 with 3 generators>
gap> invs := (1,2)(3,4)^g;
(1,2)(3,4)^G
gap> Action(a,last);
Group([ (1,7)(2,10)(3,13)(8,11)(9,14)(12,15), (1,13,4,14,5)(2,10,12,9,8)
(3,7,15,6,11), (1,2,3)(4,6,5)(7,10,13)(8,12,14)(9,11,15) ])
gap> Size(last);
120
Steve
On 20 Mar 2014, at 07:50, Farzaneh Gholaminezhad
<farzane.gholaminez...@gmail.com> wrote:
> Dear GAP forum
>
> I am Farzaneh, PhD student of Group theory and computational group theory
> I have a question about GAP please:
> would you tell me how can I restrict the Automorphism Group of a group G to
> a subset of G like the involutions of G.
> I need the order of restriction of Automorphisms of group G to the
> involution set of G.
>
> I would be so thankful if you help me.
>
> Best Regards
> Farzaneh Gholaminezhad
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