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arXiv · 1107.1826

Conjugacy growth of finitely generated groups

M. Hull·D. Osin
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Abstract

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.

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M. Hull, D. Osin. 2011-07-10. Conjugacy growth of finitely generated groups. https://arxiv.org/abs/1107.1826

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