{
  "id": "1411.1932",
  "version": "v1",
  "published": "2014-11-07T14:29:21.000Z",
  "updated": "2014-11-07T14:29:21.000Z",
  "title": "A Generalization of the $Z^*$-Theorem",
  "authors": [
    "Ellen Henke",
    "Jason Semeraro"
  ],
  "comment": "3 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Glauberman's $Z^*$-theorem and analogous statements for odd primes show that, for any prime $p$ and any finite group $G$ with Sylow $p$- subgroup $S$, the centre of $G$ is determined by the fusion system $\\mathcal{F}_S(G)$. Building on these results we show a statement that can be considered as a generalization: For any normal subgroup $N$ of $G$, the centralizer $C_S(N)$ is expressed in terms of the fusion system $\\mathcal{F}_S(G)$ and its normal subsystem induced by $N$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-07T14:29:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D20"
    ],
    "keywords": [
      "generalization",
      "fusion system",
      "finite group",
      "odd primes",
      "normal subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.1932H"
    }
  }
}