[GAP Forum] Permutations...

[Bill Allombert]

On Thu, Apr 14, 2005 at 02:43:44PM +0100, Alastair Donaldson wrote:
> 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 was you want to do is a conjugacy:

gap> (1,4)(2,5)^(1,7)(2,8);
(4,7)(5,8)

Cheers,
Bill.