On the probability of generating finite groups with a unique minimal normal subgroup

Andrea Lucchini and Fiorenza Morini

Vol. 203 (2002), No. 2, 429–440

DOI: 10.2140/pjm.2002.203.429

Abstract

Assume that a finite group G has a unique minimal normal subgroup, say N. We prove that if the order of N is large enough then the following is true: If d randomly chosen elements generate G modulo N, then these elements almost certainly generate G itself.

Milestones

Published: 1 April 2002