{
  "id": "1903.07442",
  "version": "v1",
  "published": "2019-03-18T13:49:07.000Z",
  "updated": "2019-03-18T13:49:07.000Z",
  "title": "A classification of finite locally 2-transitive generalized quadrangles",
  "authors": [
    "John Bamberg",
    "Cai Heng Li",
    "Eric Swartz"
  ],
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "Ostrom and Wagner (1959) proved that if the automorphism group $G$ of a finite projective plane $\\pi$ acts $2$-transitively on the points of $\\pi$, then $\\pi$ is isomorphic to the Desarguesian projective plane and $G$ is isomorphic to $\\mathrm{P\\Gamma L}(3,q)$ (for some prime-power $q$). In the more general case of a finite rank $2$ irreducible spherical building, also known as a \\emph{generalized polygon}, the theorem of Fong and Seitz (1973) gave a classification of the \\emph{Moufang} examples. A conjecture of Kantor, made in print in 1991, says that there are only two non-classical examples of flag-transitive generalized quadrangles up to duality. Recently, the authors made progress toward this conjecture by classifying those finite generalized quadrangles which have an automorphism group $G$ acting transitively on antiflags. In this paper, we take this classification much further by weakening the hypothesis to $G$ being transitive on ordered pairs of collinear points and ordered pairs of concurrent lines.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-18T13:49:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51E12",
      "20B05",
      "20B15",
      "20B25"
    ],
    "keywords": [
      "classification",
      "automorphism group",
      "ordered pairs",
      "isomorphic",
      "concurrent lines"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}