{
  "id": "2305.09008",
  "version": "v1",
  "published": "2023-05-15T20:45:02.000Z",
  "updated": "2023-05-15T20:45:02.000Z",
  "title": "Criteria for supersolvability of saturated fusion systems",
  "authors": [
    "Fawaz Aseeri",
    "Julian Kaspczyk"
  ],
  "comment": "20 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $p$ be a prime number. A saturated fusion system $\\mathcal{F}$ on a finite $p$-group $S$ is said to be supersolvable if there is a series $1 = S_0 \\le S_1 \\le \\dots \\le S_m = S$ of subgroups of $S$ such that $S_i$ is strongly $\\mathcal{F}$-closed for all $0 \\le i \\le m$ and such that $S_{i+1}/S_i$ is cyclic for all $0 \\le i < m$. We prove some criteria that ensure that a saturated fusion system $\\mathcal{F}$ on a finite $p$-group $S$ is supersolvable provided that certain subgroups of $S$ are abelian and weakly $\\mathcal{F}$-closed. Our results can be regarded as generalizations of purely group-theoretic results of Asaad.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-15T20:45:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "saturated fusion system",
      "supersolvability",
      "prime number",
      "purely group-theoretic results",
      "generalizations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}