UPPER BOUNDS ON THE UNIFORM SPREADS OF THE SPORADIC SIMPLE GROUPS

A finite group G has uniform spread k if there exists a fixed conjugacy class C of elements in G with the property that for any k nontrivial elements s(1), s(2), . . . , s(k) in G there exists y is an element of C such that G = < si, y > for i = 1, 2, . . . , k. Further, the exact uniform spread of G is the largest k such that G has the uniform spread k. In this paper we give upper bounds on the exact uniform spreads of thirteen sporadic simple groups.