The Conjugacy Ratio of Groups

Laura Ciobanu Radomirovic; Charles Garnet Cox; Armando Martino

doi:10.1017/S0013091518000573

The Conjugacy Ratio of Groups

Laura Ciobanu Radomirovic, Charles Garnet Cox, Armando Martino

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Abstract

In this paper we introduce and study the conjugacy ratio of a finitely generated group, which is the limit at infinity of the quotient of the conjugacy and standard growth functions. We conjecture that the conjugacy ratio is 0 for all groups except the virtually abelian ones, and confirm this conjecture for certain residually finite groups of subexponential growth, hyperbolic groups, right-angled Artin groups and the lamplighter group.

Original language	English
Pages (from-to)	895-911
Number of pages	17
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	62
Issue number	3
Early online date	22 Feb 2019
DOIs	https://doi.org/10.1017/S0013091518000573
Publication status	Published - Aug 2019

Keywords

RAAGs
conjugacy growth
degree of commutativity
hyperbolic groups
polynomial growth
wreath products

ASJC Scopus subject areas

General Mathematics

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10.1017/S0013091518000573

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This article has been published in a revised form in Proceedings of the Edinburgh Mathematical Society at: https://doi.org/10.1017/S0013091518000573. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Cambridge University Press 2019
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The Conjugacy Ratio of Groups

Abstract

Keywords

ASJC Scopus subject areas

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