{
  "id": "1611.02501",
  "version": "v1",
  "published": "2016-11-08T12:47:14.000Z",
  "updated": "2016-11-08T12:47:14.000Z",
  "title": "The Probability of Generating the Symmetric Group",
  "authors": [
    "Stefan-Christoph Virchow"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We give a new proof of Dixon's conjecture: The probability that a pair of random permutations generates either $A_n$ or $S_n$ is $1-1/n+\\mathcal {O}(n^{-\\frac{3}{2}+\\epsilon})$. Our proof is based on character theory and character estimates and does not need the classification of the finite simple groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-08T12:47:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B30",
      "20C15"
    ],
    "keywords": [
      "symmetric group",
      "probability",
      "finite simple groups",
      "random permutations generates",
      "dixons conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}