{
  "id": "0803.1746",
  "version": "v2",
  "published": "2008-03-12T11:12:10.000Z",
  "updated": "2011-07-06T06:23:44.000Z",
  "title": "Equivalences between fusion systems of finite groups of Lie type",
  "authors": [
    "Carles Broto",
    "Jesper M. M\\oller",
    "Bob Oliver"
  ],
  "comment": "20 pages, uses diagrams.sty and xy-pic, second version",
  "journal": "J. Amer. Math. Soc. 25 (2012), 1-20",
  "doi": "10.1090/S0894-0347-2011-00713-3",
  "categories": [
    "math.GR",
    "math.AT"
  ],
  "abstract": "We prove, for certain pairs G,G of finite groups of Lie type, that the p-fusion systems for G and G' are equivalent. In other words, there is an isomorphism between a Sylow p-subgroup of G and one of G' which preserves p-fusion. This occurs, for example, when G=H(q) and G'=H(q') for a simple Lie type H, and q and q' are prime powers, both prime to p, which generate the same closed subgroup of the p-adic units. Our proof uses homotopy theoretic properties of the p-completed classifying spaces of G and G', and we know of no purely algebraic proof of this result.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-07-06T06:23:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D06",
      "55R37"
    ],
    "keywords": [
      "finite groups",
      "equivalences",
      "homotopy theoretic properties",
      "simple lie type",
      "prime powers"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "J. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.1746B"
    }
  }
}