{
  "id": "2102.09165",
  "version": "v1",
  "published": "2021-02-18T05:50:22.000Z",
  "updated": "2021-02-18T05:50:22.000Z",
  "title": "On p-parts of character degrees",
  "authors": [
    "Guohua Qian",
    "Yong Yang"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "In this paper, we get the sharp bound for $|G/O_p(G)|_p$ under the assumption that either $p^2 \\nmid \\chi(1)$ for all $\\chi \\in {\\rm Irr}(G)$ or $p^2 \\nmid \\phi(1)$ for all $\\phi \\in {\\rm IBr}_p(G)$. This would settle two conjectures raised by Lewis, Navarro, Tiep, and Tong-Viet.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-18T05:50:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15",
      "20C20"
    ],
    "keywords": [
      "character degrees",
      "sharp bound",
      "assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}