[GAP Forum] building group action without losing original names?

[Dmitrii (Dima) Pasechnik]

Dear Frédéric, dear all,

On 20 December 2012 00:30, Frederic Vanhove <fvanhove at cage.ugent.be> wrote:
> Hello,
>
> I have yet another question on (equivalent) group actions.
> When I build an action on a set, is there way to have GAP store a
> bijection between the original points on which he acts, and the labels
> [1..v]?
>
> For instance, when I do:
>
> G:=SymmetricGroup(4);
> g:=AutomorphismGroup(G);
> act:=Action(g,G,OnPoints);
> Orbits(act);
>
> the output in the end is:
> [ [ 2, 7, 5, 21, 16, 13 ], [ 3, 11, 6, 9, 20, 4, 17, 14 ],
>        [ 8, 24, 23, 15, 10, 18 ], [ 12, 22, 19 ] ]

isn't the following what you need?

gap> Orbits(g,G,OnPoints);
[ [ () ], [ (1,4), (1,2), (2,4), (2,3), (1,3), (3,4) ],
  [ (1,2,4), (1,2,3), (1,4,2), (2,3,4), (1,3,2), (1,3,4), (2,4,3), (1,4,3) ],
  [ (1,3,4,2), (1,3,2,4), (1,2,3,4), (1,2,4,3), (1,4,2,3), (1,4,3,2) ],
  [ (1,3)(2,4), (1,4)(2,3), (1,2)(3,4) ] ]

HTH,
Dmitrii
>
> while elements of G itself look like (1,4)(2,3), and I would want the
> orbits in that form.
> (This is just an example, I had other more complicated sets in mind)
>

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