{
  "id": "1205.6586",
  "version": "v3",
  "published": "2012-05-30T08:48:56.000Z",
  "updated": "2015-04-24T17:37:16.000Z",
  "title": "Identifying long cycles in finite alternating and symmetric groups acting on subsets",
  "authors": [
    "Steve Linton",
    "Alice C. Niemeyer",
    "Cheryl E. Praeger"
  ],
  "comment": "45 pages",
  "categories": [
    "math.GR",
    "cs.DM"
  ],
  "abstract": "Let $H$ be a permutation group on a set $\\Lambda$, which is permutationally isomorphic to a finite alternating or symmetric group $A_n$ or $S_n$ acting on the $k$-element subsets of points from $\\{1,\\ldots,n\\}$, for some arbitrary but fixed $k$. Suppose moreover that no isomorphism with this action is known. We show that key elements of $H$ needed to construct such an isomorphism $\\varphi$, such as those whose image under $\\varphi$ is an $n$-cycle or $(n-1)$-cycle, can be recognised with high probability by the lengths of just four of their cycles in $\\Lambda$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-23T10:19:54.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-04-24T17:37:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B30",
      "60C05",
      "20P05",
      "05A05"
    ],
    "keywords": [
      "identifying long cycles",
      "symmetric groups acting",
      "finite alternating",
      "element subsets",
      "isomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.6586L"
    }
  }
}