{
  "id": "1203.2728",
  "version": "v1",
  "published": "2012-03-13T07:59:47.000Z",
  "updated": "2012-03-13T07:59:47.000Z",
  "title": "On the maximal number of coprime subdegrees in finite primitive permutation groups",
  "authors": [
    "Silvio Dolfi",
    "Robert Guralnick",
    "Cheryl Praeger",
    "Pablo Spiga"
  ],
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "The subdegrees of a transitive permutation group are the orbit lengths of a point stabilizer. For a finite primitive permutation group which is not cyclic of prime order, the largest subdegree shares a non-trivial common factor with each non-trivial subdegree. On the other hand it is possible for non-trivial subdegrees of primitive groups to be coprime, a famous example being the rank 5 action of the small Janko group on 266 points which has subdegrees of lengths 11 and 12. We prove that, for every finite primitive group, the maximal size of a set of pairwise coprime non-trivial subdegrees is at most 2.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-03-13T07:59:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B15",
      "20H30"
    ],
    "keywords": [
      "finite primitive permutation group",
      "coprime subdegrees",
      "maximal number",
      "pairwise coprime non-trivial subdegrees",
      "small janko group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.2728D"
    }
  }
}