{
  "id": "2102.10070",
  "version": "v1",
  "published": "2021-02-19T18:01:15.000Z",
  "updated": "2021-02-19T18:01:15.000Z",
  "title": "Sharp upper bounds on the minimal number of elements required to generate a transitive permutation group",
  "authors": [
    "Gareth Tracey"
  ],
  "comment": "27 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "The purpose of this paper is to prove that if $G$ is a transitive permutation group of degree $n\\geq 2$, then $G$ can be generated by $\\lfloor cn/\\sqrt{\\log{n}}\\rfloor$ elements, where $c:=\\sqrt{3}/2$. Owing to the transitive group $D_8\\circ D_8$ of degree $8$, this upper bound is best possible. Our new result improves a 2018 paper by the author, and makes use of the recent classification of transitive groups of degree $48$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-19T18:01:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B05",
      "20D05"
    ],
    "keywords": [
      "transitive permutation group",
      "sharp upper bounds",
      "minimal number",
      "transitive group",
      "classification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}