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
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