The conjugacy growth of the soluble Baumslag-Solitar groups

Laura Ciobanu; Alex Evetts; Meng Che “Turbo” Ho

The conjugacy growth of the soluble Baumslag-Solitar groups

Laura Ciobanu, Alex Evetts, Meng Che “Turbo” Ho

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we give asymptotics for the conjugacy growth of the soluble Baumslag-Solitar groups BS(1, k), k = 2, with respect to the standard generating set, by providing a complete description of geodesic conjugacy representatives. We show that the conjugacy growth series for these groups are transcendental, and give formulae for the series. As a result of our computation we also establish that in each BS(1, k) the conjugacy and standard growth rates are equal.

Original language	English
Pages (from-to)	473-495
Number of pages	23
Journal	New York Journal of Mathematics
Volume	26
Publication status	Published - 22 May 2020

Keywords

Conjugacy growth
Generating functions
Soluble groups

ASJC Scopus subject areas

General Mathematics

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http://nyjm.albany.edu/j/2020/26-23v.pdf

Cite this

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title = "The conjugacy growth of the soluble Baumslag-Solitar groups",

abstract = "In this paper we give asymptotics for the conjugacy growth of the soluble Baumslag-Solitar groups BS(1, k), k = 2, with respect to the standard generating set, by providing a complete description of geodesic conjugacy representatives. We show that the conjugacy growth series for these groups are transcendental, and give formulae for the series. As a result of our computation we also establish that in each BS(1, k) the conjugacy and standard growth rates are equal.",

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AB - In this paper we give asymptotics for the conjugacy growth of the soluble Baumslag-Solitar groups BS(1, k), k = 2, with respect to the standard generating set, by providing a complete description of geodesic conjugacy representatives. We show that the conjugacy growth series for these groups are transcendental, and give formulae for the series. As a result of our computation we also establish that in each BS(1, k) the conjugacy and standard growth rates are equal.

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KW - Generating functions

KW - Soluble groups

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The conjugacy growth of the soluble Baumslag-Solitar groups

Abstract

Keywords

ASJC Scopus subject areas

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