[GAP Forum] GAP Help to compute size of permutations

[Shubh Narayan Singh (Assistant Professor, Mathematics)]

 Thank you very much for your anticipated assistance in resolving my
problem.

Best regards
\-Shubh

On Mon, Oct 28, 2019 at 3:17 PM James Mitchell <jdm3 at st-andrews.ac.uk>
wrote:

> Dear Shubh,
>
> If you want to know the size of the group of units of your transformation
> semigroup, and you have the Semigroups package loaded, then you can simply
> type GroupOfUnits(S); where S is your transformation semigroup. If you
> don't want the group of units but only those permutations in S, then you
> can do the same thing, and just check if the elements of the GroupOfUnits
> are permutations (check DegreeOfTransformation(f) = RankOfTransformation(f)
> where f = Representative(GroupOfUnits(S))). If this is true, then every
> element of the group of units is a permutation, if this is false, then
> there are no permutations in S.
>
> Maybe this is not what you wanted, if not, then please elaborate what "all
> permutations" should mean in this context, as I can think of at least 3
> different possible meanings (2 of which are the above, the third is that
> you want to know the set of all the transformations in S that act as
> permutations on their images, which you can obtain by doing
> List(Idempotents(S), x -> HClass(S, x)); again with the Semigroups package
> loaded).
>
> Best wishes,
>
> James
>
> James Mitchell
> jdm3 at st-andrews.ac.uk
>
>
>
> > On 28 Oct 2019, at 04:36, Shubh Narayan Singh (Assistant Professor,
> Mathematics) <shubh at cub.ac.in> wrote:
> >
> > Dear all,
> >
> > Can anybody tell me a GAP code, if any, to compute the size of the set of
> > all permutations in a transformation semigroup.
> >
> > Thanks in advance for your assistance.
> >
> > --
> >
> > Sincerely,
> > *------------------------------------------*
> >
> > *Shubh N. Singh, Ph.D.Assistant Professor *
> >
> > *Department of MathematicsCentral University of South Bihar*
> >
> > *Gaya–824236 (Bihar), INDIA-----------------------------------------*
> > *E-mail: shubh at cub.ac.in <shubh at cub.ac.in>*
> > *Mob:   +91- 8404934146*
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>
>

-- 

Sincerely,
*------------------------------------------*

*Shubh N. Singh, Ph.D.Assistant Professor *

*Department of MathematicsCentral University of South Bihar*

*Gaya–824236 (Bihar), INDIA-----------------------------------------*
*E-mail: shubh at cub.ac.in <shubh at cub.ac.in>*
*Mob:   +91- 8404934146*