{
  "id": "1608.07304",
  "version": "v1",
  "published": "2016-08-25T20:32:44.000Z",
  "updated": "2016-08-25T20:32:44.000Z",
  "title": "Characterization of intersecting families of maximum size in $PSL(2,q)$",
  "authors": [
    "Ling Long",
    "Rafael Plaza",
    "Peter Sin",
    "Qing Xiang"
  ],
  "comment": "32 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We consider the action of the $2$-dimensional projective special linear group $PSL(2,q)$ on the projective line $PG(1,q)$ over the finite field $F_q$, where $q$ is an odd prime power. A subset $S$ of $PSL(2,q)$ is said to be an intersecting family if for any $g_1,g_2 \\in S$, there exists an element $x\\in PG(1,q)$ such that $x^{g_1}= x^{g_2}$. It is known that the maximum size of an intersecting family in $PSL(2,q)$ is $q(q-1)/2$. We prove that all intersecting families of maximum size are cosets of point stabilizers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-25T20:32:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "intersecting family",
      "maximum size",
      "dimensional projective special linear group",
      "characterization",
      "odd prime power"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}