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arXiv · 1908.05321

The conjugacy growth of the soluble Baumslag-Solitar groups

Laura Ciobanu·Alex Evetts·Meng-Che "Turbo" Ho
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Abstract

In this paper we give asymptotics for the conjugacy growth of the soluble Baumslag-Solitar groups $BS(1,k)$, $k\geq 2$, 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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Laura Ciobanu, Alex Evetts, Meng-Che "Turbo" Ho. 2019-08-14. The conjugacy growth of the soluble Baumslag-Solitar groups. https://arxiv.org/abs/1908.05321

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