{
  "abstract": "Let $G$ be a finite $2$-transitive permutation group. We determine the orbits of $G$ on the unordered triples of its point set, together with the three-point stabilizer and its image inside $S_3$, for every affine and almost simple family in the finite $2$-transitive classification. These data classify the $G$-invariant triple systems and the simple $2$-\\mbox{$(v,3,λ)$} designs admitting $G$, and yield in a uniform way the standard objects attached to them: the incidence and block graphs (with arc-transitivity and strong regularity in the Steiner case), the constant-weight and design codes, and the Schurian coherent configurations on triples.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15340",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhilin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6jzqvnjkym8qq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15340",
  "fulltext_url": null,
  "id": "6jzqvnjkym8qq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15340",
  "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": "W7221762980",
  "pdf_url": "https://arxiv.org/pdf/2610.15340",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6jzqvnjkym8qq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15340",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15340"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Three-point orbits of 2-transitive groups and their combinatorial applications",
  "title_text": "Three-point orbits of 2-transitive groups and their combinatorial applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/6jzqvnjkym8qq",
  "venue": "arXiv",
  "versions": []
}