Dear Forum,
On Sun, Feb 11, 2007 at 04:03:22PM +0200, Michael Fridman wrote to the GAP Forum: > I have a question about the Reidemeister-Schreier method. I know that the > function > PresentationSubgroupRrs( G, cosettable ) requires a presentation of the > group G and the coset-table. I saw that the coset-table is given by a > table of permutations. However, in my case, I have only the explicit > representatives of the subgroup H in G > (so, I have only a representation of G and set of representatives of G/H, > and I need to find a presentation of H). is there a function that can > covert these representatives to permutations? Or is there another version > of PresentationSubgroupRrs? > > Thanks in advance > Michael Friedman In a private letter to M.F. on January 12 I pointed to a Forum letter by Derek Holt of June 7, 2006, in which, as much as I understood, he had answered the same question, pointing out that such an algorithm cannot exist. I asked M. F. if I had misunderstood his question. Since I got no answer, I think that this is not the case, and so here for the sake of closing the case in the Forum: Such an algorithm cannot exist since different, in fact even nonisomorphic, subgroups can have the same transversal (set of coset representatives). The smallest example is given by the dihedral group of order 8 in which the cyclic subgroup C of order 4 and one of the two elementary abelian subgroups of order 4 , say V, both have either of the two cyclic subgroups of order 2 not contained in V as transversals. Kind regards Joachim Neubueser _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
