The conjugacy growth of the soluble Baumslag-Solitar groups

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

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)473-495
Number of pages23
JournalNew York Journal of Mathematics
Volume26
Publication statusPublished - 22 May 2020

Keywords

  • Conjugacy growth
  • Generating functions
  • Soluble groups

ASJC Scopus subject areas

  • Mathematics(all)

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