The exact spread of the Mathieu group M 11

Abstract

Following [J. I. Brenner and J. Wiegold. Two-generator groups, I. Michigan Math. J. 22 (1975), 53–64.], we define the exact spread of a group G to be the greatest integer r for which, given any r non-identity elements of G, one can find y ∈ G such that 〈xi = y〉 = G for i = 1, 2, …, r. In this paper, we determine the exact spread of M11, the smallest sporadic simple group of Mathieu.