## Abstract

It is known that the subgroup growth of finitely generated linear groups is either polynomial or at least {Mathematical expression}. In this paper we prove the existence of a finitely generated group whose subgroup growth is of type {Mathematical expression}. This is the slowest non-polynomial subgroup growth obtained so far for finitely generated groups. The subgroup growth type n^{ log n} is also realized. The proofs involve analysis of the subgroup structure of finite alternating groups and finite simple groups in general. For example, we show there is an absolute constant c such that, if T is any finite simple group, then T has at most n^{ c log n} subgroups of index n.

Original language | English |
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Pages (from-to) | 399-418 |

Number of pages | 20 |

Journal | Israel Journal of Mathematics |

Volume | 96 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1996 |