{
  "id": "1311.3906",
  "version": "v1",
  "published": "2013-11-15T16:25:46.000Z",
  "updated": "2013-11-15T16:25:46.000Z",
  "title": "Finite primitive permutation groups and regular cycles of their elements",
  "authors": [
    "Michael Giudici",
    "Cheryl E. Praeger",
    "Pablo Spiga"
  ],
  "comment": "Dedicated to the memory of our friend \\'Akos Seress 22 pages: Conjecture 1.2 has been recently solved (paper is in preparation)",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "We conjecture that if $G$ is a finite primitive group and if $g$ is an element of $G$, then either the element $g$ has a cycle of length equal to its order, or for some $r,m$ and $k$, the group $G\\leq S_m\\wr S_r$, preserving a product structure of $r$ direct copies of the natural action of $S_m$ or $A_m$ on $k$-sets. In this paper we reduce this conjecture to the case that $G$ is an almost simple group with socle a classical group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-15T16:25:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite primitive permutation groups",
      "regular cycles",
      "simple group",
      "length equal",
      "finite primitive group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.3906G"
    }
  }
}