{
  "id": "1804.10513",
  "version": "v1",
  "published": "2018-04-25T21:19:21.000Z",
  "updated": "2018-04-25T21:19:21.000Z",
  "title": "2-Parts of real class sizes",
  "authors": [
    "Hung P. Tong-Viet"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We investigate the structure of finite groups whose non-central real class sizes have the same $2$-part. In particular, we prove that such groups are solvable and have $2$-length one. As a consequence, we show that a finite group is solvable if it has two real class sizes. This confirms a conjecture due to G. Navarro, L. Sanus and P. Tiep.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-25T21:19:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E45",
      "20D10"
    ],
    "keywords": [
      "finite group",
      "non-central real class sizes",
      "consequence",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}