[GAP Forum] Listing idempotents in terms of generators

[Shubh Narayan Singh (Assistant Professor, Mathematics)]

Dear Sir,

I am trying to elaborate my question:

Let f:= Transformation([2,3,4,5,1])    g:=Transformation([5,4,5,1,1]),  and
S:=Semigroup(f, g);

We observed that the idempotent h:= Transformation([1,1,1,1,1]) belongs to
the semigroup S
which can be written in terms of functions f and g. That is   h = g^2 f^4 g.

I am searching for the gap code for listing the idempotents in terms of the
transformations f and g as above example.


On Fri, Jul 14, 2017 at 4:45 PM, James Mitchell <jdm3 at st-andrews.ac.uk>
wrote:

> Dear Shubh,
>
> Do you mean you want to factorise the idempotents over the transformations
> f and g? If so, then you can do this using the semigroups package as
> follows:
>
> S := Semigroup(f, g);
> List(Idempotents(S), x -> Factorisation(S, x));
>
> Best wishes,
>
> James
>
> On Fri, 14 Jul 2017 at 12:08 Shubh Narayan Singh (Assistant Professor,
> Mathematics) <shubh at cub.ac.in> wrote:
>
>> Let M be transformation monoid generated by two transformations f and g on
>> the finite set.
>>
>> Please can someone tell the gap code, if exists, for listing all the
>> idempotents in terms of the transformations f and g.
>>
>>
>> Thank you in advance.
>>
>> \-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 <+91%2084049%2034146>*
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>


-- 
-- 
*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*