{
  "id": "1508.00039",
  "version": "v1",
  "published": "2015-07-31T21:38:50.000Z",
  "updated": "2015-07-31T21:38:50.000Z",
  "title": "Derangements in finite classical groups for actions related to extension field and imprimitive subgroups and the solution of the Boston-Shalev conjecture",
  "authors": [
    "Jason Fulman",
    "Robert Guralnick"
  ],
  "comment": "24 pages",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "This is the fourth paper in a series. We prove a conjecture made independently by Boston et al and Shalev. The conjecture asserts that there is an absolute positive constant delta such that if G is a finite simple group acting transitively on a set of size n > 1, then the proportion of derangements in G is greater than delta. We show that with possibly finitely many exceptions, one can take delta = .016. Indeed, we prove much stronger results showing that for many actions, the proportion of derangements goes to 1 as n increases and prove similar results for families of permutation representations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-31T21:38:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite classical groups",
      "extension field",
      "boston-shalev conjecture",
      "imprimitive subgroups",
      "derangements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150800039F"
    }
  }
}