Dear GAP Forum, Jerry Swan asked
> For some element g of a group G for which irr := > IrreducibleRepresentations(G) have been obtained, is it possible to > recover > g from images := List(irr,r->Image(r,g)) ? and later added > Concretely, I'm working with $S_n$, which I should have clarified. If phi is a group homomorphism and you know phi( g ) for some group element g in the source of phi then the set of preimages of phi( g ) under phi consists of the coset g ker( phi ). If phi is faithful (and S_n has faithful irreducible representations) then just take the unique preimage under phi. In general, if you know the images of g under sufficiently many (irreducible) representations phi_i such that the intersection of their kernels is trivial then you can determine g from the intersection of the preimages of the phi_i( g ). All the best, Thomas _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
