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] 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).

^*The second author was supported by research grants from URF (University of Natal) and NRF (South Africa).

ACKNOWLEDGMENT

The authors express their gratitude to Prof. Robert M. Guralnick whose suggestions and comments led to significant improvement of the content and the presentation of this paper.

Notes

^*The second author was supported by research grants from URF (University of Natal) and NRF (South Africa).