[GAP Forum] Action with fixed points

[justine.falque at lilo.org]

Dear GAP community,

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.)

I can imagine ways to do this, but not very efficiently, even less
elegantly. Can someone help me with this issue ?

Thank you very much !