[GAP Forum] Permutations...

[Alastair Donaldson]

Dear GAP forum

Suppose I have two permutations, alpha and beta, which both act on 
{1,..,n} for some n>0.

Consider the disjoint cycle form of alpha.  I want to get the permutation 
which has the same d.c.f. as alpha, except that each occurrence of a 
number k in this d.c.f. is replaced with k^beta.

For example, suppose alpha = (1,4)(2,5) and beta = (1,7)(2,8) then I want 
the permutation (1^beta,4^beta)(2^beta,5^beta), i.e. (7,4)(8,5).

I think I could implement this by turning alpha into a list 
representation, applying beta to each element in the list, permuting the 
indices of elements using beta, and turning the resulting list back into 
the permutation.  I just wondered if anyone knows of an easier (or 
existing) way to do this with GAP.

Thanks in advance

Alastair.