Conjugacy growth series of some wreath products

Abstract

In this paper we consider groups of the form $G\wr L$, where the set of generators naturally extends the sets of generators of $G$ and $L$, and $L$ admits a Cayley graph that is a tree. We show how one can compute the conjugacy growth series of such groups in terms of the standard and conjugacy growth series of $G$. We then provide explicit formulas for groups of the form $G\wr \mathbb{Z}$ and $G\wr (C_2\ast C_2)$. We also prove that the radius of convergence of the conjugacy growth series of $G\wr L$, for any $G$ and $L$ as above, is the same as the radius of convergence of its standard growth series.

arXiv comment26 pages, 6 figures

References in corpus (1)

• Formal conjugacy growth in acylindrically hyperbolic groups

Cited by in corpus (1)

• The conjugacy growth of the soluble Baumslag-Solitar groups