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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In memory of our teacher, colleague, and friend, Shimshon Amitsur
This research was supported by The Israel Science Foundation, administered by The Israel Accademy of Science and Humanities.
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Mann, A., Shalev, A. Simple groups, maximal subgroups, and probabilistic aspects of profinite groups. Israel J. Math. 96, 449–468 (1996). https://doi.org/10.1007/BF02937317
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DOI: https://doi.org/10.1007/BF02937317