[GAP Forum] Wreath Product for Monoids

[Attila Egri-Nagy]

Hi,

It seems that my previous answer made it to the Forum archive, but it
was not dispatched to Forum members.
Here it is:

Dear Jan Philip,

With the development version of the SgpDec package,
https://bitbucket.org/dersu/sgpdec, you can simply do

gap> S1 := Semigroup(Transformation([5,4,2,2,2]),
Transformation([2,3,4,4,5]));
<semigroup with 2 generators>
gap> S2 := Semigroup(Transformation([6,5,4,2,2,2]),
Transformation([6,2,3,4,4,5]));
<semigroup with 2 generators>

gap> S1wrS2 := SemigroupWreathProduct(S1,S2);
<wreath product of semigroups>
gap> Size(S1wrS2);
9143008

This gives the wreath product represented as the full cascade product,
definitions here: http://arxiv.org/abs/1303.0091

However, you already heard the bad news: it is in the development
version. Please let me know if you need help to set it up.

best,
attila

On Tue, May 14, 2013 at 7:30 AM, Alexander Hulpke
<hulpke at math.colostate.edu> wrote:
>
>
> Dear Forum, Dear Jan-Philip W"achter,
>
>> WreathProduct only accepts groups as arguments. Is there a way to calculate
>> the wreath product of two (finite) monoids?
>
> The GAP library only provides methods to construct wreath products of (finite) groups. It would be possible to install methods for monoids using InstallOtherMethod, but I am not aware of such code. Your bet bet might be to simply construct the wreath product ``by hand''.
>
>    Best,
>
>       Alexander Hulpke
>
>
>
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