[GAP Forum] Action with fixed points

[Hulpke,Alexander]

Dear Forum, Dear Justine Falque,

I need to compute the action of a specific group on a specific set,
but the Action function ignores fixed points, which is an issue in
my context.

To clarify, say I have the set {a,b,c,d} (actually a list in my
program) with natural action of the group generated by the
transposition (a,c). I would like a way to obtain this action as the
group generated by (1,3), and not the group generated by (1,2).
(Ideally it would also remember that its degree is 4 but since I
provide the set I have an easy access to this information.)

As for the Action, that is what should happen:

gap> l:=[1,6,3,7,8,2];
[ 1, 6, 3, 7, 8, 2 ]
gap> g:=SymmetricGroup(3);
Sym( [ 1 .. 3 ] )
gap> Action(g,l);
Group([ (1,6,3), (1,6) ])

(If this is not the case, please send us a stand-alone example of this haappening to support at gap-system.org<mailto:support at gap-system.org>)

The degree however, by definition, will always be the number of moved points, so if you want to include fixed points you would have to keep track of this yourself.

Best wishes,

 Alexander Hulpke