The Conjugacy Growth of the Soluble Baumslag-Solitar Groups

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

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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 languageEnglish
Pages (from-to)473-495
JournalNew York Journal of Mathematics
Publication statusPublished - 22 May 2020


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