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 <j...@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 > j...@st-andrews.ac.uk > > > > > On 28 Oct 2019, at 04:36, Shubh Narayan Singh (Assistant Professor, > Mathematics) <sh...@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: sh...@cub.ac.in <sh...@cub.ac.in>* > > *Mob: +91- 8404934146* > > _______________________________________________ > > Forum mailing list > > Forum@gap-system.org > > https://mail.gap-system.org/mailman/listinfo/forum > > -- Sincerely, *------------------------------------------* *Shubh N. Singh, Ph.D.Assistant Professor * *Department of MathematicsCentral University of South Bihar* *Gaya–824236 (Bihar), INDIA-----------------------------------------* *E-mail: sh...@cub.ac.in <sh...@cub.ac.in>* *Mob: +91- 8404934146* _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
