{
  "abstract": "We establish three results on decision problems for finitely generated matrix groups, based on fiber products: $\\bullet$ The torsion-freeness problem is undecidable for subgroups of $\\mathrm{SL}_{4}(\\mathbb{Z})$, $\\bullet$ There exists a finitely generated subgroup $G$ of $\\mathrm{SL}_{4}(\\mathbb{Z})$ with undecidable square root problem, $\\bullet$ No algorithm can, on input a tuple of invertible matrices, output the list of marked finite quotients of the group they generate.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15378",
  "author_total": 2,
  "authors": [
    {
      "name": "Ruiwen Dong"
    },
    {
      "name": "Emmanuel Rauzy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fj18bc61dnx1z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15378",
  "fulltext_url": null,
  "id": "fj18bc61dnx1z",
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  "landing_url": "https://arxiv.org/abs/2609.15378",
  "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",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7213266650",
  "pdf_url": "https://arxiv.org/pdf/2609.15378",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fj18bc61dnx1z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15378",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15378"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Torsion-freeness problem for matrix groups",
  "title_text": "Torsion-freeness problem for matrix groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/fj18bc61dnx1z",
  "venue": "arXiv",
  "versions": []
}