[GAP Forum] Cartesian Group Direct Product

[Alexander Hulpke]

Dear GAP-Forum, Dear Paul Hjelmstad,

> Thanks, I know about that one. And you need to make them both  
> Permutation Groups,
> BTW, but what I really need is a Cartesian style (cross) product,  
> as  a Group Direct Product,
> I tried Semidirect Product but that doesn't seem to be it either.

`DirectProduct' will work for any pair of groups. It will choose a  
representation that is most efficient, i.e. for two permutation groups  
it will represent the product as permutation group of larger degree.

The functions `Embedding' and `Projection' create the natural maps  
that allom composition or decomposition acording to the form as  
cartesian product. I.e.
e1:=Embedding(product,1);
e2:=Embedding(product,2);
Then Image(e1,x) gives the first component of x as element of the  
diurect product, Image(e2,x) the second component.

Anything that could be done using a formal product represnetation can  
be done with these maps.

Best,

     Alexander Hulpke