{
  "id": "2102.00448",
  "version": "v1",
  "published": "2021-01-31T13:25:39.000Z",
  "updated": "2021-01-31T13:25:39.000Z",
  "title": "Orbits of Sylow subgroups of finite permutation groups",
  "authors": [
    "John Bamberg",
    "Alexander Bors",
    "Alice Devillers",
    "Michael Giudici",
    "Cheryl E. Praeger",
    "Gordon F. Royle"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We say that a finite group $G$ acting on a set $\\Omega$ has Property $(*)_p$ for a prime $p$ if $P_\\omega$ is a Sylow $p$-subgroup of $G_\\omega$ for all $\\omega\\in\\Omega$ and Sylow $p$-subgroups $P$ of $G$. Property $(*)_p$ arose in the recent work of Tornier (2018) on local Sylow $p$-subgroups of Burger-Mozes groups, and he determined the values of $p$ for which the alternating group $A_n$ and symmetric group $S_n$ acting on $n$ points has Property $(*)_p$. In this paper, we extend this result to finite $2$-transitive groups and we give a structural characterisation result for the finite primitive groups that satisfy Property $(*)_p$ for an allowable prime $p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-31T13:25:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B05",
      "20B15"
    ],
    "keywords": [
      "finite permutation groups",
      "sylow subgroups",
      "structural characterisation result",
      "burger-mozes groups",
      "finite primitive groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}