{
  "id": "2204.04311",
  "version": "v1",
  "published": "2022-04-08T22:08:18.000Z",
  "updated": "2022-04-08T22:08:18.000Z",
  "title": "On the generation of simple groups by Sylow subgroups",
  "authors": [
    "Timothy C. Burness",
    "Robert M. Guralnick"
  ],
  "comment": "17 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a finite simple group of Lie type and let $P$ be a Sylow $2$-subgroup of $G$. In this paper, we prove that for any nontrivial element $x \\in G$, there exists $g \\in G$ such that $G = \\langle P, x^g \\rangle$. By combining this result with recent work of Breuer and Guralnick, we deduce that if $G$ is a finite nonabelian simple group and $r$ is any prime divisor of $|G|$, then $G$ is generated by a Sylow $2$-subgroup and a Sylow $r$-subgroup.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-08T22:08:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sylow subgroups",
      "finite nonabelian simple group",
      "generation",
      "finite simple group",
      "nontrivial element"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}