{
  "abstract": "The Tits alternative asserts that a finitely generated linear group is either solvable-by-finite or contains a non-abelian free subgroup. Given a non-solvable-by-finite subgroup G of GL(d, F), where F is the field of complex numbers or a non-archimedean local field, we present methods to construct explicitly a non-abelian 2-generator free subgroup of G in specific cases. Our implementations in the computeralgebra system Oscar are publicly available.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03175",
  "author_total": 5,
  "authors": [
    {
      "name": "Emmanuel Breuillard"
    },
    {
      "name": "Bettina Eick"
    },
    {
      "name": "Tommy Hofmann"
    },
    {
      "name": "Derek Holt"
    },
    {
      "name": "Eamonn O'Brien"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b3dvwars0nwb5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03175",
  "fulltext_url": null,
  "id": "b3dvwars0nwb5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03175",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03175",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b3dvwars0nwb5.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03175",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03175"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Constructing free subgroups of matrix groups",
  "title_text": "Constructing free subgroups of matrix groups",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/b3dvwars0nwb5",
  "venue": "arXiv",
  "versions": []
}