Formal conjugacy growth in graph products I

TL;DR

This paper derives a recursive formula for conjugacy growth series in graph products and shows conditions under which conjugacy and standard growth rates are equal, advancing understanding of algebraic growth properties.

Contribution

It introduces a recursive formula for conjugacy growth series in graph products and establishes conditions for equality of conjugacy and standard growth rates.

Findings

Recursive formula for conjugacy growth series

Equality of conjugacy and standard growth rates under certain conditions

Results applicable to standard generating sets

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.