Let G be a finite group and, for n (Formula Presented) N, denote by mn (G) the number of maximal subgroups of G with index n. Let (Formula Presented] and let E1 (G) be the expected number of elements of G which have to be drawn at random, with replacement, before a set of generators is found. Then (Formula Presented).
Generation of finite groups and maximal subgroup growth
Lucchini A.;Moscatiello M.
2020
Abstract
Let G be a finite group and, for n (Formula Presented) N, denote by mn (G) the number of maximal subgroups of G with index n. Let (Formula Presented] and let E1 (G) be the expected number of elements of G which have to be drawn at random, with replacement, before a set of generators is found. Then (Formula Presented).
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