{
  "id": "1807.03550",
  "version": "v1",
  "published": "2018-07-10T09:39:46.000Z",
  "updated": "2018-07-10T09:39:46.000Z",
  "title": "Conjugacy classes, characters and products of elements",
  "authors": [
    "Robert M. Guralnick",
    "Alexander Moretó"
  ],
  "comment": "9 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Recently, Baumslag and Wiegold proved that a finite group $G$ is nilpotent if and only if $o(xy)=o(x)o(y)$ for every $x,y\\in G$ of coprime order. Motivated by this result, we study the groups with the property that $(xy)^G=x^Gy^G$ and those with the property that $\\chi(xy)=\\chi(x)\\chi(y)$ for every complex irreducible character $\\chi$ of $G$ and every nontrivial $x, y \\in G$ of pairwise coprime order. We also consider several ways of weakening the hypothesis on $x$ and $y$. While the result of Baumslag and Wiegold is completely elementary, some of our arguments here depend on (parts of) the classification of finite simple groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-10T09:39:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15",
      "20D15",
      "20E45"
    ],
    "keywords": [
      "conjugacy classes",
      "finite simple groups",
      "pairwise coprime order",
      "complex irreducible character",
      "finite group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}