The conjugacy growth of the soluble Baumslag-Solitar groups

摘要

In this paper we give asymptotics for the conjugacy growth of the soluble Baumslag-Solitar groups BS(1,k), k>1, 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.