{
  "id": "0811.3666",
  "version": "v1",
  "published": "2008-11-22T08:11:07.000Z",
  "updated": "2008-11-22T08:11:07.000Z",
  "title": "A characteristic subgroup for fusion systems",
  "authors": [
    "Silvia Onofrei",
    "Radu Stancu"
  ],
  "comment": "LaTeX file, 19 pages",
  "journal": "Journal of Algebra 322 (2009) 1705-1718",
  "doi": "10.1016/j.jalgebra.2009.05.026",
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "As a counterpart for the prime 2 to Glauberman's $ZJ$-theorem, Stellmacher proves that any nontrivial 2-group $S$ has a nontrivial characteristic subgroup $W(S)$ with the following property. For any finite $\\Sigma_4$-free group $G$, with $S$ a Sylow 2-subgroup of $G$ and with $O_2(G)$ self-centralizing, the subgroup $W(S)$ is normal in $G$. We generalize Stellmacher's result to fusion systems. A similar construction of $W(S)$ can be done for odd primes and gives rise to a Glauberman functor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-22T08:11:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D15",
      "20E25"
    ],
    "keywords": [
      "fusion systems",
      "nontrivial characteristic subgroup",
      "free group",
      "odd primes",
      "similar construction"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.3666O"
    }
  }
}