Groups with super-exponential subgroup growth |
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Authors: | L Pyber A Shalev |
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Institution: | (1) Mathematical Institute, Hungarian Academy of Sciences, P.O.B. 127, H-1364 Budapest, Hungary;(2) Institute of Mathematics, Hebrew University, 91904 Jerusalem, Israel |
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Abstract: | We show that, if the subgroup growth of a finitely generated (abstract or profinite) groupG is super-exponential, then every finite group occurs as a quotient of a finite index subgroup ofG. The proof involves techniques from finite permutation groups, and depends on the Classification of Finite Simple Groups.The first author was partially supported by the Hungarian National Foundation for Scientific Research, Grant No. T7441. The second author was partially supported by the Israeli National Science Foundation. |
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Keywords: | primary: 20E07 20E26 secondary: 20B35 20E18 |
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