{
  "id": "1402.4981",
  "version": "v3",
  "published": "2014-02-20T12:24:19.000Z",
  "updated": "2014-11-17T10:35:00.000Z",
  "title": "Centralizers of Subsystems of Fusion Systems",
  "authors": [
    "Jason Semeraro"
  ],
  "comment": "9 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "When $(S,\\mathcal{F},\\mathcal{L})$ is a $p$-local finite group and $(T,\\mathcal{E},\\mathcal{\\L}_0)$ is weakly normal in $(S,\\mathcal{F},\\mathcal{L})$ we show that a definition of $C_S(\\mathcal{E})$ given by Aschbacher has a simple interpretation from which one can deduce existence and strong closure very easily. We also appeal to a result of Gross to give a new proof that there is a unique fusion system $C_{\\mathcal{F}}(\\mathcal{E})$ on $C_S(\\mathcal{E})$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-29T13:10:11.000Z",
      "title": "Centralisers of Subsystems of Fusion Systems",
      "abstract": "When $(S,\\mathcal{F},\\mathcal{L})$ is a $p$-local finite group and $(T,\\mathcal{E},\\mathcal{L}_0) \\unlhd (S,\\mathcal{F},\\mathcal{L})$ we define an $S$-centraliser $C_S(\\mathcal{L}_0)$ of $\\mathcal{L}_0$ in $S$ and observe that this is equivalent to a definition of $C_S(\\mathcal{E})$ given by Aschbacher. We also appeal to a result of Gross to give a new proof that there is a unique fusion system $C_{\\mathcal{F}}(\\mathcal{E})$ on $C_S(\\mathcal{E})$.",
      "comment": "11 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-11-17T10:35:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "centralizers",
      "subsystems",
      "local finite group",
      "unique fusion system",
      "simple interpretation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.4981S"
    }
  }
}