{
  "id": "2302.05203",
  "version": "v1",
  "published": "2023-02-10T12:12:41.000Z",
  "updated": "2023-02-10T12:12:41.000Z",
  "title": "Proving a conjecture for fusion systems on a class of groups",
  "authors": [
    "Patrick Serwene"
  ],
  "categories": [
    "math.GR",
    "math.RT"
  ],
  "abstract": "We prove that the conjecture that exotic and block-exotic fusion systems coincide holds all for all fusion systems on p-groups of maximal nilpotency class, where p is either a small prime or $p \\geq 5$ and the group is also exceptional. For $p = 3$, this is achieved by considering exotic fusion systems described by Diaz--Ruiz--Viruel. For $p \\geq 5$, this is achieved by proving a family of exotic fusion systems discovered by Parker and Stroth is also block-exotic. Together with a previous result by the author, which we also generalise in this paper, and a result by Grazian and Parker this implies the conjecture for fusion systems on such groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-10T12:12:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conjecture",
      "block-exotic fusion systems coincide holds",
      "maximal nilpotency class",
      "considering exotic fusion systems",
      "small prime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}