{
  "id": "1205.5290",
  "version": "v1",
  "published": "2012-05-23T20:59:34.000Z",
  "updated": "2012-05-23T20:59:34.000Z",
  "title": "The Galois group of random elements of linear groups",
  "authors": [
    "Alexander Lubotzky",
    "Lior Rosenzweig"
  ],
  "categories": [
    "math.NT",
    "math.GR",
    "math.RT"
  ],
  "abstract": "Let F be a finitely generated field of characteristic zero and \\Gamma<GL_n(F) a finitely generated subgroup. For an element g in \\Gamma, let Gal(F(g)/ F) be the Galois group of the splitting field of the characteristic polynomial of g over F. We show that the structure of Gal(F(g)/ F) has a typical behaviour depending on F, and on the geometry of the Zariski closure of \\Gamma (but not on \\Gamma).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-23T20:59:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "galois group",
      "random elements",
      "linear groups",
      "characteristic zero",
      "zariski closure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.5290L"
    }
  }
}