{
  "id": "1904.06545",
  "version": "v1",
  "published": "2019-04-13T13:14:10.000Z",
  "updated": "2019-04-13T13:14:10.000Z",
  "title": "Groups with few $p'$-character degrees",
  "authors": [
    "Eugenio Giannelli",
    "Noelia Rizo",
    "Mandi Schaeffer Fry"
  ],
  "categories": [
    "math.GR",
    "math.RT"
  ],
  "abstract": "We prove a variation of Thompson's Theorem. Namely, if the first column of the character table of a finite group $G$ contains only two distinct values not divisible by a given prime number $p>3$, then $O^{pp'pp'}(G)=1$. This is done by using the classification of finite simple groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-13T13:14:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "character degrees",
      "finite simple groups",
      "first column",
      "finite group",
      "thompsons theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}