{
  "id": "1907.06425",
  "version": "v1",
  "published": "2019-07-15T10:53:12.000Z",
  "updated": "2019-07-15T10:53:12.000Z",
  "title": "Flag-transitive non-symmetric $2$-designs with $(r,λ)=1$ and exceptional groups of Lie type",
  "authors": [
    "Yongli Zhang",
    "Shenglin Zhou"
  ],
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "This paper determined all pairs $(\\mathcal{D},G)$ where $\\mathcal{D}$ is a non-symmetric 2-$(v,k,\\lambda)$ design with $(r,\\lambda)=1$ and $G$ is the almost simple flag-transitive automorphism group of $\\mathcal{D}$ with an exceptional socle of Lie type. We prove that if $T\\trianglelefteq G\\leq Aut(T)$ where $T$ is an exceptional group of Lie type, then $T$ must be the Ree group or Suzuki group, and there are five classes of non-isomorphic designs $\\mathcal{D}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-15T10:53:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lie type",
      "exceptional group",
      "flag-transitive non-symmetric",
      "simple flag-transitive automorphism group",
      "ree group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}