Groups whose subgroup growth is less than linear

Aner Shalev*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Let G be a residually finite group and let an(G) denote the number of index n subgroups of G. It is shown that an(G)/n → 0 if and only if G has a finite index central subgroup whose finite quotients are all cyclic. As an application we show that the degree of a group of polynomial subgroup growth cannot lie strictly between 0 and 1.

Original languageAmerican English
Pages (from-to)77-91
Number of pages15
JournalInternational Journal of Algebra and Computation
Volume7
Issue number1
DOIs
StatePublished - Feb 1997

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