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The conjugacy ratio of groups

The conjugacy ratio of groups
The conjugacy ratio of groups
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.
Conjugacy growth, degree of commutativity, hyperbolic groups, wreath products
Ciobanu, Laura
903a79bf-8399-4e14-94a7-61689766a0cd
Cox, Charles
9c613e52-7d80-4f93-b231-321517188655
Martino, Armando
65f1ff81-7659-4543-8ee2-0a109be286f1
Ciobanu, Laura
903a79bf-8399-4e14-94a7-61689766a0cd
Cox, Charles
9c613e52-7d80-4f93-b231-321517188655
Martino, Armando
65f1ff81-7659-4543-8ee2-0a109be286f1

Ciobanu, Laura, Cox, Charles and Martino, Armando (2018) The conjugacy ratio of groups. Proceedings of the Edinburgh Mathematical Society. (doi:10.1017/S0013091518000573).

Record type: Article

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.

Text
1709.02152 - Accepted Manuscript
Available under License University of Southampton Accepted Manuscript Licence.
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More information

Submitted date: 1 September 2017
Accepted/In Press date: 10 May 2018
e-pub ahead of print date: 2018
Related URLs:
Keywords: Conjugacy growth, degree of commutativity, hyperbolic groups, wreath products

Identifiers

Local EPrints ID: 420629
URI: http://eprints.soton.ac.uk/id/eprint/420629
DOI: doi:10.1017/S0013091518000573
PURE UUID: 1e156828-fab4-46ca-adb5-58a89b7353c3
ORCID for Armando Martino: ORCID iD orcid.org/0000-0002-5350-3029

Catalogue record

Date deposited: 11 May 2018 16:30
Last modified: 16 Mar 2024 06:36

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Contributors

Author: Laura Ciobanu
Author: Charles Cox
Author: Armando Martino ORCID iD

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