[GAP Forum] automorphisms and stabilizers

[Mowsey]

You can specify your own function for the action. The point in using
some of the existing actions is that special more efficient methods
are available for some. Since you may not expect there to be such
methods already installed, you can just use the generic:

  G   := SmallGroup(8,4);;
  A   := AutomorphismGroup(G);;
  V   := Subgroup(G,[G.1]);;
  A_V := Stabilizer(A,V,function(sub,aut) return Image(aut,sub); end);;


On Fri, November 4, 2005 17:18, Ryan Higginbottom wrote:
> Dear GAP folks:
>
> Any help you can give me on this question would be appreciated.  I'm
> fairly new to using GAP, so the answer might be simple, but I've searched
> a bit on the GAP site without finding an immediate answer.  Forgive me if
> this is trivial.
>
> The automorphism group of a group G acts on the set S of subgroups of G.
> Given a particular subgroup V of G, I would like to compute the size of
> Aut(G)_V, that is, the stabilizer in Aut(G) of V.
>
> I cannot figure out how to establish the proper action in this situation.
> I think that I will need something like the ExternalSet command, because
> this doesn't look like a commonly used action (based on what I've seen in
> the manual).  This seems like an easy computation though.  Can anyone
> help?
>
> Thank you.
>
> Ryan Higginbottom