{
  "abstract": "A transitive permutation group $G\\le\\Sym(\\Pcal)$ is said to have the Siemons--Wagner property $\\star_3$ if some three-point subset has a $G$-orbit longer than the orbit of every four-point subset containing it. In this paper we develop a structural theory of three-point orbits of finite $2$-transitive groups (orbit-length hierarchies, pointwise and setwise stabilizers, and their geometric realisations, including the unital and the ovoid), and we use it to completely settle Bradley's conjecture: a finite primitive group of degree at least $8$ satisfying $\\star_3$ is isomorphic to $\\PSL(2,7)$ or $\\PGL(2,7)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24502",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhilin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9b0hrj91p3z68.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24502",
  "fulltext_url": null,
  "id": "9b0hrj91p3z68",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24502",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7223060959",
  "pdf_url": "https://arxiv.org/pdf/2610.24502",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9b0hrj91p3z68.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24502",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24502"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Siemons--Wagner property and Bradley's conjecture",
  "title_text": "The Siemons--Wagner property and Bradley's conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/9b0hrj91p3z68",
  "venue": "arXiv",
  "versions": []
}