Alan, By far the fastest practical way to check if you got S_n is to find few (pseudo)random elements, and compute their orders. When doing this, it's important not to trigger a computation of the strong stab. chain. Here is a snippet from my old GAP files :
# q is a group gprimes:=function(q) local ra, i; ra:=[]; for i in [1..500] do ra:=Union(FactorsInt(Order(PseudoRandom(q))),ra); od; return ra; end; Roughly speaking, the primes occurring will provide a fingerprint matching S_n. I can't recall who invented this simple trick. HTH, Dmitrii _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
