{
  "abstract": "We prove the existence of non-sofic Tarski monsters of every sufficiently large prime exponent and of torsion-free non-sofic Tarski monsters. The proof combines a theorem of Sandhu--Thom with quotient theorems of Semenov. These groups are minimal non-sofic, since all their proper subgroups are cyclic. A theorem of Minasyan--Osin--Witzel gives continuum many pairwise non-quasi-isometric torsion-free simple examples. Kulikova's quotient theorem also yields non-simple minimal non-sofic groups of exponent $p^m$ for every $m\\geq2$ and every sufficiently large prime $p$. We then study descending chains of non-sofic subgroups in other constructions. We give proper self-embeddings of the binary Leavitt unit group, higher Brin--Thompson groups and the hyperbolic group studied by Douglas and Mghirbi. The explicit Kun--Thom wreath products and doubles are locally graded. These examples are $ω$-non-sofic, and the locally graded ones contain no minimal non-sofic subgroup.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.42140",
  "author_total": 1,
  "authors": [
    {
      "name": "Kıvanç Ersoy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1jxyyv7kbrh61.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.42140",
  "fulltext_url": null,
  "id": "1jxyyv7kbrh61",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.42140",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.42140",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1jxyyv7kbrh61.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.42140",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.42140"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Non-sofic Tarski monsters",
  "title_text": "Non-sofic Tarski monsters",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/1jxyyv7kbrh61",
  "venue": "arXiv",
  "versions": []
}