{
  "id": "2006.11660",
  "version": "v1",
  "published": "2020-06-20T21:31:16.000Z",
  "updated": "2020-06-20T21:31:16.000Z",
  "title": "Finite groups with some restriction on the vanishing set",
  "authors": [
    "Sesuai Madanha",
    "Bernardo Rodrigues"
  ],
  "comment": "9 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $ x $ be an element of a finite group $ G $ and denote the order of $ x $ by $ \\mathrm{ord}(x) $. We consider a finite group $ G $ such that $ \\gcd(\\mathrm{ord}(x),\\mathrm{ord}(y))\\leqslant 2 $ for any two vanishing elements $ x $ and $ y $ contained in distinct conjugacy classes. We show that such a group $ G $ is solvable. When $ G $ with the property above is supersolvable, we show that $ G $ has a normal metabelian $ 2 $-complement.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-20T21:31:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15"
    ],
    "keywords": [
      "finite group",
      "vanishing set",
      "restriction",
      "distinct conjugacy classes",
      "normal metabelian"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}