# Conjugacy growth of finitely generated groups

Authors
Type
Published Article
Publication Date
Jan 27, 2015
Submission Date
Jul 09, 2011
Identifiers
arXiv ID: 1107.1826
Source
arXiv
We show that every non-decreasing function $f\colon \mathbb N\to \mathbb N$ bounded from above by $a^n$ for some $a\ge 1$ can be realized (up to a natural equivalence) as the conjugacy growth function of a finitely generated group. We also construct a finitely generated group $G$ and a subgroup $H\le G$ of index 2 such that $H$ has only 2 conjugacy classes while the conjugacy growth of $G$ is exponential. In particular, conjugacy growth is not a quasi-isometry invariant.