{
  "id": "1303.5998",
  "version": "v3",
  "published": "2013-03-24T21:41:22.000Z",
  "updated": "2014-10-25T22:02:02.000Z",
  "title": "A characterization of the 2-fusion system of L_4(q)",
  "authors": [
    "Justin Lynd"
  ],
  "comment": "v1: 37 pages; v2: many minor corrections/changes in response to anonymous referee report, section 1 shortened slightly; v3: minor updates",
  "categories": [
    "math.GR"
  ],
  "abstract": "We study a saturated fusion system F on a finite 2-group S having a Baumann component based on a dihedral 2-group. Assuming F is 2-perfect with no nontrivial normal 2-subgroups, and the centralizer of the component is a cyclic 2-group, it is shown that F is uniquely determined as the 2-fusion system of L_4(q_1) for some q_1 = 3 (mod 4). This should be viewed as a contribution to a program recently outlined by M. Aschbacher for the classification of simple fusion systems at the prime 2. The corresponding problem in the component-type portion of the classification of finite simple groups (the L_2(q), A_7 standard form problem) was one of the last to be completed, and was ultimately only resolved in an inductive context with heavy artillery. Thanks primarily to requiring the component to be Baumann, our main arguments by contrast require only 2-fusion analysis and transfer. We deduce a companion result in the category of groups.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-02T22:56:29.000Z",
      "comment": "v1: 37 pages; v2: many minor corrections/changes in response to anonymous referee report, Section 1 shortened slightly. Comments welcome",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-10-25T22:02:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D20",
      "20D05"
    ],
    "keywords": [
      "characterization",
      "simple fusion systems",
      "finite simple groups",
      "standard form problem",
      "nontrivial normal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.5998L"
    }
  }
}