{
  "abstract": "Let $\\mathcal{Q}$ be a finite thick generalized quadrangle of order $(s,t)$ with a flag-transitive automorphism group $G$. A well-known conjecture of Kantor from the early 1990s asserts that up to duality, $\\mathcal{Q}$ is either of classical type, or it is one of two sporadic examples of order $(3,5)$ or $(15,17)$. Although this fundamental problem in finite geometry remains open, it has been resolved in some special cases. For example, a theorem of Buekenhout and Van Maldeghem from 1994 proves Kantor's conjecture under the stronger assumption that $G$ acts distance-transitively on the set of points of $\\mathcal{Q}$. In this paper, we study Kantor's conjecture in the setting where $G$ acts primitively on both the points and lines of $\\mathcal{Q}$. Here a theorem of Bamberg et al. implies that $G$ is almost simple with socle $X$ a finite simple group of Lie type, and several special cases where the Lie rank of $X$ is at most $2$ have recently been settled in a sequence of papers. Our main theorem resolves the problem for all almost simple groups of Lie type, thereby completing the proof of Kantor's conjecture for generalized quadrangles with a flag-transitive automorphism group acting primitively on points and lines.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38819",
  "author_total": 3,
  "authors": [
    {
      "name": "Timothy C. Burness"
    },
    {
      "name": "Tao Feng"
    },
    {
      "name": "Jianbing Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cbhjb0tj25ymc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38819",
  "fulltext_url": null,
  "id": "cbhjb0tj25ymc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38819",
  "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.CO"
    ],
    [
      "arxiv",
      "math.GR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38819",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cbhjb0tj25ymc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38819",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38819"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Primitive flag-transitive generalized quadrangles",
  "title_text": "Primitive flag-transitive generalized quadrangles",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/cbhjb0tj25ymc",
  "venue": "arXiv",
  "versions": []
}