{
  "id": "1406.1702",
  "version": "v1",
  "published": "2014-06-06T15:13:11.000Z",
  "updated": "2014-06-06T15:13:11.000Z",
  "title": "Finite primitive groups and regular orbits of group elements",
  "authors": [
    "Simon Guest",
    "Pablo Spiga"
  ],
  "comment": "21 pages",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "We prove that if $G$ is a finite primitive permutation group and if $g$ is an element of $G$, then either $g$ has a cycle of length equal to its order, or for some $r$, $m$ and $k$, the group $G \\leq \\mathrm{Sym}(m) \\textrm{wr} \\mathrm{Sym}(r)$ preserves the product structure of $r$ direct copies of the natural action of $\\mathrm{Sym}(m)$ on $k$-sets. This gives an answer to a question of Siemons and Zalesski and a solution to a conjecture of Giudici, Praeger and the second author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-06T15:13:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite primitive groups",
      "regular orbits",
      "group elements",
      "finite primitive permutation group",
      "length equal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.1702G"
    }
  }
}