{
  "id": "1003.4722",
  "version": "v2",
  "published": "2010-03-24T19:43:14.000Z",
  "updated": "2010-04-13T15:12:16.000Z",
  "title": "On finite groups whose Sylow subgroups have a bounded number of generators",
  "authors": [
    "Colin D. Reid"
  ],
  "comment": "7 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let G be a finite non-nilpotent group such that every Sylow subgroup of G is generated by at most d elements, and such that p is the largest prime dividing |G|. We show that G has a non-nilpotent image G/N, such that N is characteristic and of index bounded by a function of d and p. This result will be used to prove that the index of the Frattini subgroup of G is bounded in terms of d and p. Upper bounds will be given explicitly for soluble groups.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-04-13T15:12:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sylow subgroup",
      "finite groups",
      "bounded number",
      "generators",
      "finite non-nilpotent group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.4722R"
    }
  }
}