[GAP Forum] Constructing wreath products (and other things)

[Alexander Hulpke]

Dear Martyn,

On Sep 30, 2005, at 9:43 AM, Martyn Quick wrote:

> I'm trying to construct a wreath product in such a way I can find  
> my standard generators very easily.
>
> For example, I've just tried:
>
> A := CyclicGroup(3);
> B := CyclicGroup(9);
> W := WreathProduct(A,B)
>
> which all seems fine... but how do I get hold of my favourite  
> generators for this wreath product?  (i.e., an element in the base  
> group and an element generating my top group).

You want to use `Embedding'. If B is a permutation group of degree n,  
then
Embedding(W,1)  to Embedding(W,n) are maps from A into the n copies  
of A in W.
Embedding(W,n+1) is a map from B to the chosen complement.

(Projection(W) is a map from W to B).

Then using `Image', you can get map your favourite generators of A  
and B into W.

Best,

    Alexander