{
  "id": "1507.06724",
  "version": "v1",
  "published": "2015-07-24T02:07:31.000Z",
  "updated": "2015-07-24T02:07:31.000Z",
  "title": "On p-parts of character degrees and conjugacy class sizes of finite groups",
  "authors": [
    "Yong Yang",
    "Guohua Qian"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1501.03237",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a finite group and $Irr(G)$ the set of irreducible complex characters of $G$. Let $e_p(G)$ be the largest integer such that $p^{e_p(G)}$ divides $\\chi(1)$ for some $\\chi \\in Irr(G)$. We show that $|G:\\mathbf{F}(G)|_p \\leq p^{k e_p(G)}$ for a constant $k$. This settles a conjecture of A. Moret\\'o. We also study the related problems of the $p$-parts of conjugacy class sizes of finite groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-24T02:07:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C20",
      "20C15",
      "20D10"
    ],
    "keywords": [
      "conjugacy class sizes",
      "finite group",
      "character degrees",
      "largest integer",
      "irreducible complex characters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150706724Y"
    }
  }
}