{
  "id": "2203.09261",
  "version": "v1",
  "published": "2022-03-17T11:29:27.000Z",
  "updated": "2022-03-17T11:29:27.000Z",
  "title": "Flag-transitive, point-imprimitive symmetric $2$-$(v,k,λ)$ designs with $k>λ\\left(λ-3 \\right)/2$",
  "authors": [
    "Alessandro Montinaro"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\mathcal{D}=\\left(\\mathcal{P},\\mathcal{B} \\right)$ be a symmetric $2$-$(v,k,\\lambda )$ design admitting a flag-transitive, point-imprimitive automorphism group $G$ that leaves invariant a non-trivial partition $\\Sigma$ of $\\mathcal{P}$. Praeger and Zhou \\cite{PZ} have shown that, there is a constant $k_{0}$ such that, for each $B \\in \\mathcal{B}$ and $\\Delta \\in \\Sigma$, the size of $\\left\\vert B \\cap \\Delta \\right \\vert$ is either $0$ or $k_{0}$. In the present paper we show that, if $k>\\lambda \\left(\\lambda-3 \\right)/2$ and $k_{0} \\geq 3$, $\\mathcal{D}$ is isomorphic to one of the known flag-transitive, point-imprimitive symmetric $2$-designs with parameters $(45,12,3)$ or $(96,20,4)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-17T11:29:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "point-imprimitive symmetric",
      "flag-transitive",
      "non-trivial partition",
      "point-imprimitive automorphism group",
      "leaves invariant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}