Hi, I'm interested in studying certain groups which arise as permutations of subsets of a given group. As a simple example, let G be any finite group, and S = G x G, the set of pairs of elements of G. Define a to be the permutation of S generated by (x,y) --> (x,xy) and b to be the one generated by (x,y) --> (yx,y). Is there a simple way to construct the subgroup of the permutation group on S generated by a and b? In this case both a and b have order exp(G) & for example I'd like to be able to compute a presentation for the group of permutations they generate. More generally I'd like to study other operations on certain subsets (or sequences) of elements derived from a fixed group G.
As permutation groups seem to be given as permutations of sets of integers, it almost seems that I should (in essence) have to describe a one-to-one correspondence of S with a set of integers [1..m] and describe a and b by explicitly computing via this correspondence. Is that sort of thing really necessary? It usually seems that there are built-in operations in GAP to avoid such. Perhaps I'm missing something obvious. Suggestions most welcome! Keith _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
