{
  "id": "1901.07048",
  "version": "v1",
  "published": "2019-01-21T19:25:27.000Z",
  "updated": "2019-01-21T19:25:27.000Z",
  "title": "Centers of Sylow Subgroups and Automorphisms",
  "authors": [
    "Robert Guralnick",
    "Gabriel Navarro"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Suppose that p is an odd prime and G is a finite group having no normal non-trivial p'-subgroup. We show that if a is an automorphism of G of p-power order centralizing a Sylow p-group of G, then a is inner. This answers a conjecture of Gross.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-21T19:25:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D20",
      "20E32"
    ],
    "keywords": [
      "sylow subgroups",
      "automorphism",
      "odd prime",
      "normal non-trivial",
      "sylow p-group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}