Formal conjugacy growth in graph products I

Authors

Laura Ciobanu,, Heriot-Watt University
Susan Hermiller, University of Nebraska - LincolnFollow
Valentin Mercier, Universidade Nova de Lisboa

Date of this Version

3-15-2023

Citation

Groups Geom. Dyn. 17 (2023), 427–457 DOI 10.4171/GGD/704

Comments

Used by permission.

Abstract

In this paper we give a recursive formula for the conjugacy growth series of a graph product in terms of the conjugacy growth and standard growth series of subgraph products. We also show that the conjugacy and standard growth rates in a graph product are equal provided that this property holds for each vertex group. All results are obtained for the standard generating set consisting of the union of generating sets of the vertex groups.