{
  "abstract": "We prove that the group $G=\\mathbb{Z}[1/2]^3\\rtimes(\\operatorname{SL}_3(\\mathbb{Z})\\times\\mathbb{Z})$ is finitely presented and residually finite, but is not stable in finite actions, answering a question of Gohla and Thom. The proof uses the infranormal Kazhdan subgroup $H=\\mathbb{Z}^3\\rtimes\\operatorname{SL}_3(\\mathbb{Z})$ and its normal closure $N$ in $G$. A Kazhdan projection estimate shows that, in any $G$-action weakly contained in finite actions, every $H$-invariant measurable subset is also $N$-invariant. We construct an explicit sofic approximation of $G$ whose limit action contains a measurable subset that is $H$-invariant but not $N$-invariant.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35841",
  "author_total": 1,
  "authors": [
    {
      "name": "Jonas Pinke"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7jkzf6z1tn67c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35841",
  "fulltext_url": null,
  "id": "7jkzf6z1tn67c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35841",
  "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"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7223862616",
  "pdf_url": "https://arxiv.org/pdf/2610.35841",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7jkzf6z1tn67c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:43Z",
      "native_id": "2610.35841",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35841"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Infranormal Kazhdan subgroups and instability in finite actions",
  "title_text": "Infranormal Kazhdan subgroups and instability in finite actions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:43Z",
  "url": "https://research.draconitic.com/paper/7jkzf6z1tn67c",
  "venue": "arXiv",
  "versions": []
}