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.
|Number of pages||23|
|Journal||New York Journal of Mathematics|
|Publication status||Published - 22 May 2020|
- Conjugacy growth
- Generating functions
- Soluble groups
ASJC Scopus subject areas