{
  "id": "2011.14426",
  "version": "v1",
  "published": "2020-11-29T19:37:29.000Z",
  "updated": "2020-11-29T19:37:29.000Z",
  "title": "The maximal number of elements pairwise generating the symmetric group of even degree",
  "authors": [
    "Francesco Fumagalli",
    "Martino Garonzi",
    "Attila Maróti"
  ],
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "Let $G$ be the symmetric group of even degree at least $26$. We compute the maximal size of a subset $S$ of $G$ such that $\\langle x,y \\rangle = G$ whenever $x,y \\in S$ and $x \\neq y$, and we show that it is equal to the covering number of $G$, that is, to the minimal number of proper subgroups of $G$ whose union is $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-29T19:37:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B15",
      "20B30",
      "20B40",
      "20D60",
      "05D40"
    ],
    "keywords": [
      "symmetric group",
      "elements pairwise generating",
      "maximal number",
      "minimal number",
      "proper subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}