{
  "abstract": "This note record a finitely generated extension of Caprace's example of a non-inner-amenable group is also not properly proximal, which answers the original question by Boutonnet, Ioana and Peterson. The extension is an explicit ICC subgroup of $\\operatorname{GL}_4(\\mathbb{F}_2(t))$, which has no property \\textup{(T)}. Failure of proper proximality follows from the work of Ishan-Peterson-Ruth and the passage of proper proximality to co-amenable subgroups. Non-inner-amenability follows from a property-\\textup{(T)} subgroup and an elementary centralizer computation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30158",
  "author_total": 1,
  "authors": [
    {
      "name": "Xin Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5z0pm7q1cnvmq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30158",
  "fulltext_url": null,
  "id": "5z0pm7q1cnvmq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30158",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7214395451",
  "pdf_url": "https://arxiv.org/pdf/2609.30158",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5z0pm7q1cnvmq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.30158",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30158"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A finitely generated ICC non property (T) group that is neither inner amenable nor properly proximal",
  "title_text": "A finitely generated ICC non property (T) group that is neither inner amenable nor properly proximal",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/5z0pm7q1cnvmq",
  "venue": "arXiv",
  "versions": []
}