ON THE SPREAD OF THE SPORADIC SIMPLE GROUPS

Abstract

A group is 2-generated if it can be generated by two elements x and y. In this case y is called a mate for x. Brenner and Wiegold defined a finite group G to have spread r. A group is said to have exact spread r if it has spread r but not r + 1. The exact spread of a group G is denoted by s(G). Ganief [11] Ganief, S. 1996. 2-Generations of the Sporadic Simple Groups, Ph.D Thesis University of Natal. [Google Scholar] in his PhD thesis proved that if G is a sporadic simple group, then s(G) ≥ 2. In this paper, by using probabilistic methods, for each sporadic simple group G we find a reasonable lower bound for s(G).