Simple groups,maximal subgroups,and probabilistic aspects of profinite groups |
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Authors: | Avinoam Mann Aner Shalev |
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Institution: | 1. Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram, 91904, Jerusalem, Israel
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Abstract: | We show that a finite simple group has at mostn 1.875+o(1) maximal subgroups of indexn. 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. |
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