[GAP Forum] Regarding Idempotent elements in semigroup

[Shubh Narayan Singh (Assistant Professor, Mathematics)]

Thank you sir for providing the code with clarification.

Regards,

\-Shubh

On Fri, Jul 7, 2017 at 11:41 AM, Vinay Wagh <waghoba at gmail.com> wrote:

> gap> a:= Transformation( [ 2, 3, 4, 1 ] );;
> gap> b:= Transformation( [ 2, 2, 3, 4 ] );;
> gap> s:= Semigroup(a, b);
> <transformation semigroup of degree 4 with 2 generators>
> gap> l := Idempotents( s );
> [ Transformation( [ 2, 2 ] ), IdentityTransformation, Transformation(
> [ 1, 1, 3, 3 ] ), Transformation( [ 4, 2, 2, 4 ] ),
>   Transformation( [ 1, 2, 3, 1 ] ), Transformation( [ 1, 2, 4, 4 ] ),
> Transformation( [ 1, 3, 3 ] ), Transformation( [ 1, 1 ] ),
>   Transformation( [ 2, 2, 2 ] ), Transformation( [ 2, 2, 3, 3 ] ),
> Transformation( [ 2, 2, 4, 4 ] ), Transformation( [ 3, 3, 3 ] ),
>   Transformation( [ 4, 2, 3, 4 ] ), Transformation( [ 1, 3, 3, 1 ] ),
> Transformation( [ 2, 2, 3, 2 ] ), Transformation( [ 2, 2, 2, 2 ] ),
>   Transformation( [ 1, 1, 1 ] ), Transformation( [ 1, 1, 4, 4 ] ),
> Transformation( [ 3, 3, 3, 3 ] ), Transformation( [ 4, 4, 3, 4 ] ),
>   Transformation( [ 1, 1, 3, 1 ] ), Transformation( [ 1, 2, 2, 1 ] ),
> Transformation( [ 4, 3, 3, 4 ] ), Transformation( [ 1, 2, 3, 3 ] ),
>   Transformation( [ 3, 2, 3, 3 ] ), Transformation( [ 4, 2, 4, 4 ] ),
> Transformation( [ 1, 2, 1, 1 ] ), Transformation( [ 1, 2, 2 ] ),
>   Transformation( [ 1, 3, 3, 3 ] ), Transformation( [ 1, 4, 4, 4 ] ),
> Transformation( [ 4, 4, 4, 4 ] ), Transformation( [ 1, 1, 1, 1 ] ),
>   Transformation( [ 1, 2, 2, 2 ] ) ]
> gap> Size( l );
> 33
>
>
> Hope this helps!
>
> VInay
>
>
>
>
> On 7 July 2017 at 06:56, Shubh Narayan Singh (Assistant Professor,
> Mathematics) <shubh at cub.ac.in> wrote:
> > Please can someone tell the gap code, if exists,  for
> >
> > 1.  listing all the idempotent elements
> >
> > 2. cardinality of the set of all idempotent elements
> >
> > in a finite semigroup.
> >
> > Thank you in advance.
> >
> >
> > *Regards,*
> >
> > *Shubh*
> >
> >
> > *-----------------------------------------------------Shubh Narayan
> Singh,
> > Ph.D.Assistant Professor *
> >
> >
> >
> > *Department of MathematicsCentral University of South BiharPatna - 800
> > 014-----------------------------------------*
> > *e-mail: shubh at cub.ac.in <shubh at cub.ac.in>*
> > *Mob:   +91- 8404934146*
> > _______________________________________________
> > Forum mailing list
> > Forum at mail.gap-system.org
> > http://mail.gap-system.org/mailman/listinfo/forum
>



-- 
-- 
*Sincerely,*
*Shubh Narayan Singh*


*-----------------------------------------------------Shubh Narayan Singh,
Ph.D.Assistant Professor *



*Department of MathematicsCentral University of South BiharPatna - 800
014-----------------------------------------*
*e-mail: shubh at cub.ac.in <shubh at cub.ac.in>*
*Mob:   +91- 8404934146*