Simple groups, maximal subgroups, and probabilistic aspects of profinite groups

Avinoam Mann*, Aner Shalev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

38 Scopus citations

Abstract

We show that a finite simple group has at most n 1.875+o(1) maximal subgroups of index n. This enables us to characterise profinite groups which are generated with positive probability by boundedly many random elements. It turns out that these groups are exactly those having polynomial maximal subgroup growth. Related results are also established.

Original languageAmerican English
Pages (from-to)449-468
Number of pages20
JournalIsrael Journal of Mathematics
Volume96
Issue number2
DOIs
StatePublished - Jun 1996

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