{
  "id": "1905.07431",
  "version": "v1",
  "published": "2019-05-17T18:37:02.000Z",
  "updated": "2019-05-17T18:37:02.000Z",
  "title": "Rational Groups and a Characterization of a Class of Permutation Groups",
  "authors": [
    "Cecil Andrew Ellard"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We prove that a finite group is rational if and only if it has a set of permutation characters which separate conjugacy classes. It follows from this that a finite group is rational if and only if it has a representation as a permutation group in which any two elements fixing the same number of letters are conjugate.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-17T18:37:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "permutation group",
      "rational groups",
      "characterization",
      "finite group",
      "separate conjugacy classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}