Non-inner amenability of the Higman-Thompson groups

Eli Bashwinger; Matthew C. B. Zaremsky

Non-inner amenability of the Higman-Thompson groups

Group Theory 2025-07-22 v2

Authors: Eli Bashwinger , Matthew C. B. Zaremsky

Abstract

We prove that the Higman-Thompson groups $T_n$ and $V_n$ are non-inner amenable for all $n\ge 2$ . This extends Haagerup and Olesen's result that Thompson's groups $T=T_2$ and $V=V_2$ are non-inner amenable. Their proof relied on machinery only available in the $n=2$ case, namely Thurston's piecewise-projective model for Thompson's group $T$ , so our approach necessarily utilizes different tools. This also provides an alternate proof of Haagerup-Olesen's result when $n=2$ .

Keywords

higman-thompson groups non-inner amenability thompson groups piecewise-projective model

Cite

@article{arxiv.2203.13798,
  title  = {Non-inner amenability of the Higman-Thompson groups},
  author = {Eli Bashwinger and Matthew C. B. Zaremsky},
  journal= {arXiv preprint arXiv:2203.13798},
  year   = {2025}
}

Comments

10 pages, 2 figures. v2: minor changes, accepted version, to appear in IJAC

Non-inner amenability of the Higman-Thompson groups

Abstract

Keywords

Cite

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