{
  "id": "2011.03804",
  "version": "v1",
  "published": "2020-11-07T16:37:00.000Z",
  "updated": "2020-11-07T16:37:00.000Z",
  "title": "On the degrees of irreducible characters fixed by some field automorphism",
  "authors": [
    "Nicola Grittini"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "It is known that, if all the irreducible real valued characters of a finite group are of odd degree, then the group has a normal Sylow 2-subgroup. In this paper, we prove and analogous result for solvable groups, by taking into account the degree of irreducible characters fixed by some field isomorphism of prime order $p$. We prove it as a consequence of a more general result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-07T16:37:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15"
    ],
    "keywords": [
      "irreducible characters",
      "field automorphism",
      "irreducible real valued characters",
      "prime order",
      "field isomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}