{
  "id": "2203.13798",
  "version": "v1",
  "published": "2022-03-25T17:35:01.000Z",
  "updated": "2022-03-25T17:35:01.000Z",
  "title": "Non-inner amenability of the Higman-Thompson groups",
  "authors": [
    "Eli Bashwinger",
    "Matthew C. B. Zaremsky"
  ],
  "comment": "10 pages, 2 figures",
  "categories": [
    "math.GR"
  ],
  "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 $n=2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-25T17:35:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "higman-thompson groups",
      "non-inner amenability",
      "thompsons group",
      "extends haagerup",
      "approach necessarily utilizes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}