{
  "id": "1605.01068",
  "version": "v1",
  "published": "2016-05-03T20:02:14.000Z",
  "updated": "2016-05-03T20:02:14.000Z",
  "title": "Permutations contained in transitive subgroups",
  "authors": [
    "Sean Eberhard",
    "Kevin Ford",
    "Dimitris Koukoulopoulos"
  ],
  "comment": "33 pages, 1 figure",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "In the first paper in this series we estimated the probability that a random permutation $\\pi\\in\\mathcal{S}_n$ has a fixed set of a given size. In this paper, we elaborate on the same method to estimate the probability that $\\pi$ has $m$ disjoint fixed sets of prescribed sizes $k_1,\\dots,k_m$, where $k_1+\\cdots+k_m=n$. We deduce an estimate for the proportion of permutations contained in a transitive subgroup other than $\\mathcal{S}_n$ or $\\mathcal{A}_n$. This theorem consists of two parts: an estimate for the proportion of permutations contained in an imprimitive transitive subgroup, and an estimate for the proportion of permutations contained in a primitive subgroup other than $\\mathcal{S}_n$ or $\\mathcal{A}_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-03T20:02:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "20B30",
      "20B15"
    ],
    "keywords": [
      "transitive subgroup",
      "proportion",
      "probability",
      "random permutation",
      "disjoint fixed sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}