{
  "id": "1903.06817",
  "version": "v1",
  "published": "2019-03-15T22:09:58.000Z",
  "updated": "2019-03-15T22:09:58.000Z",
  "title": "The Largest Prime Dividing the Maximal Order of an Element of $S_n$",
  "authors": [
    "Jon Grantham"
  ],
  "journal": "Mathematics of Computation 64 (1995), 407-410",
  "doi": "10.1090/S0025-5718-1995-1270619-3",
  "categories": [
    "math.NT"
  ],
  "abstract": "We define $g(n)$ to be the maximal order of an element of the symmetric group on $n$ elements. Results about the prime factorization of $g(n)$ allow a reduction of the upper bound on the largest prime divisor of $g(n)$ to $1.328\\sqrt{n\\log n}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-15T22:09:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N56",
      "11N05",
      "20B30"
    ],
    "keywords": [
      "largest prime dividing",
      "maximal order",
      "largest prime divisor",
      "symmetric group",
      "upper bound"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Math. Comp."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}