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The degree of commutativity and lamplighter groups

The degree of commutativity and lamplighter groups
The degree of commutativity and lamplighter groups

The degree of commutativity of a group G measures the probability of choosing two elements in G which commute. There are many results studying this for finite groups. In [Y. Antolín, A. Martino and E. Ventura, Degree of commutativity of infinite groups, Proc. Amer. Math. Soc. 145 (2017) 479-485, MR 3577854], this was generalized to infinite groups. In this note, we compute the degree of commutativity for wreath products of the form Z Z and F Z, where F is any finite group.

degree of commutativity, exponential growth, lamplighter group, Wreath products
0218-1967
Cox, Charles Garnet
522d9ea0-0890-41c6-848a-bcd0a45e2fca
Cox, Charles Garnet
522d9ea0-0890-41c6-848a-bcd0a45e2fca

Cox, Charles Garnet (2018) The degree of commutativity and lamplighter groups. International Journal of Algebra and Computation. (doi:10.1142/S0218196718500510).

Record type: Article

Abstract

The degree of commutativity of a group G measures the probability of choosing two elements in G which commute. There are many results studying this for finite groups. In [Y. Antolín, A. Martino and E. Ventura, Degree of commutativity of infinite groups, Proc. Amer. Math. Soc. 145 (2017) 479-485, MR 3577854], this was generalized to infinite groups. In this note, we compute the degree of commutativity for wreath products of the form Z Z and F Z, where F is any finite group.

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More information

Accepted/In Press date: 28 June 2018
e-pub ahead of print date: 10 August 2018
Keywords: degree of commutativity, exponential growth, lamplighter group, Wreath products

Identifiers

Local EPrints ID: 424193
URI: https://eprints.soton.ac.uk/id/eprint/424193
ISSN: 0218-1967
PURE UUID: d5f56482-d0b3-4fb1-ba2b-dd46fa8034b7

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Date deposited: 05 Oct 2018 11:34
Last modified: 05 Oct 2018 11:34

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