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On Groups with Slow Intersection Growth

Part of: Special aspects of infinite or finite groups Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  14 November 2016

Martin Kassabov  and
Francesco Matucci
Martin Kassabov
Affiliation:
Department of Mathematics, Cornell University Malott Hall, Ithaca, NY 14850, USA
Francesco Matucci
Affiliation:
Département de Mathématiques, Faculté des Sciences d'Orsay, Université Paris Sud 11, Bâtiment 425, Orsay, France (francesco.matucci@gmail.com)
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Abstract

Intersection growth concerns the asymptotic behaviour of the index of the intersection of all subgroups of a group that have index at most n. In this paper we show that the intersection growth of some groups may not be a nicely behaved function by showing the following seemingly contradictory results: (a) for any group G the intersection growth function iG(n) is super linear infinitely often, and (b) for any non-decreasing unbounded function f there exists a group G such that the graph of iG is below the one of f infinitely often.

Keywords

residually finite groupsgrowth in groupsintersection growthresidual finiteness growth

MSC classification

Secondary: 20F69: Asymptotic properties of groups 20E07: Subgroup theorems; subgroup growth 20E26: Residual properties and generalizations; residually finite groups
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 2 , May 2017 , pp. 387 - 390
Copyright
Copyright © Edinburgh Mathematical Society 2017 

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