Title: Random sets which invariably generate the symmetric group
Abstract: If x1, x2,…, xr is a list of elements from a group G then we say that this list has some property P 'invariably' if y1, y2,…, yr has property P whenever yi is conjugate in G to xi fo i = 1,2,…, r. A problem in computational Galois theory gives riseto the following questions. Suppose that r elements are chosen independently and uniformly at random from the symmetric group Sn. On the average, how large must r be in order that this list of elements will invariably generate a transitive group, and how large must r be in order that the list will invariably generate Sn? It is shown that on the average r = O((logn)12) is sufficient in both cases, but numerical evidence suggests that in fact r = O(1) may be enough.