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.
On the probability of generating finite groups with a unique minimal normal subgroup
LUCCHINI, ANDREA;
2002
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.
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