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Degree of commutativity of infinite groups

Degree of commutativity of infinite groups
Degree of commutativity of infinite groups
We prove that, in a finitely generated residually finite group of subexponential growth, the proportion of commuting pairs is positive if and only if the group is virtually abelian. In particular, this covers the case where the group has polynomial growth (i.e., virtually nilpotent groups). We also show that for non-elementary hyperbolic groups, the proportion of commuting pairs is always zero.
0002-9939
479-485
Antolin, Yago
2ff7c13c-8a0d-4a50-9de5-63a750896e4c
Martino, Armando
65f1ff81-7659-4543-8ee2-0a109be286f1
Ventura, Enric
543ad8f8-4af2-41c5-91ec-7781d79bf647
Antolin, Yago
2ff7c13c-8a0d-4a50-9de5-63a750896e4c
Martino, Armando
65f1ff81-7659-4543-8ee2-0a109be286f1
Ventura, Enric
543ad8f8-4af2-41c5-91ec-7781d79bf647

Antolin, Yago, Martino, Armando and Ventura, Enric (2017) Degree of commutativity of infinite groups. Proceedings of the American Mathematical Society, 145, 479-485. (doi:10.1090/proc/13231).

Record type: Article

Abstract

We prove that, in a finitely generated residually finite group of subexponential growth, the proportion of commuting pairs is positive if and only if the group is virtually abelian. In particular, this covers the case where the group has polynomial growth (i.e., virtually nilpotent groups). We also show that for non-elementary hyperbolic groups, the proportion of commuting pairs is always zero.

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More information

Accepted/In Press date: 3 April 2016
e-pub ahead of print date: 28 July 2016
Published date: 1 February 2017
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 402877
URI: http://eprints.soton.ac.uk/id/eprint/402877
DOI: doi:10.1090/proc/13231
ISSN: 0002-9939
PURE UUID: 486a69d0-a564-4b1c-81ed-ff1edab8409e
ORCID for Armando Martino: ORCID iD orcid.org/0000-0002-5350-3029

Catalogue record

Date deposited: 17 Nov 2016 14:22
Last modified: 15 Mar 2024 03:32

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Contributors

Author: Yago Antolin
Author: Armando Martino ORCID iD
Author: Enric Ventura

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