[GAP Forum] Regarding Idempotent elements in semigroup

[Vinay Wagh]

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*
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