{
  "id": "2001.04728",
  "version": "v1",
  "published": "2020-01-14T12:00:17.000Z",
  "updated": "2020-01-14T12:00:17.000Z",
  "title": "On flag-transitive 2-(v,k,2) designs",
  "authors": [
    "Alice Devillers",
    "Hongxue Liang",
    "Cheryl E. Praeger",
    "Binzhou Xia"
  ],
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "This paper is devoted to the classification of flag-transitive 2-(v,k,2) designs. We show that apart from two known symmetric 2-(16,6,2) designs, every flag-transitive subgroup G of the automorphism group of a nontrivial 2-(v,k,2) design is primitive of affine or almost simple type. Moreover, we classify the 2-(v,k,2) designs admitting a flag transitive almost simple group G with socle PSL(n,q) for some n \\geq 3. Alongside this analysis, we give a construction for a flag-transitive 2-(v,k-1,k-2) design from a given flag-transitive 2-(v,k,1) design which induces a 2-transitive action on a line. Taking the design of points and lines of the projective space PG(n-1,3) as input to this construction yields a G-flag-transitive 2-(v,3,2) design where G has socle PSL(n,3) and v=(3^n-1)/2. Apart from these designs, our PSL-classification yields exactly one other example, namely the complement of the Fano plane.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-14T12:00:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B05",
      "05B25",
      "20B25"
    ],
    "keywords": [
      "flag-transitive",
      "socle psl",
      "simple type",
      "simple group",
      "automorphism group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}