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

Pure Mathematics

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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 formulas 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
Journal	New York Journal of Mathematics
Volume	26
Publication status	Published - 22 May 2020

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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 formulas 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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AU - Ho, Meng-Che “Turbo”

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N2 - 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 formulas 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.

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 formulas 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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VL - 26

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EP - 495

JO - New York Journal of Mathematics

JF - New York Journal of Mathematics

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The Conjugacy Growth of the Soluble Baumslag-Solitar Groups

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