{
  "id": "2002.02103",
  "version": "v1",
  "published": "2020-02-06T05:43:46.000Z",
  "updated": "2020-02-06T05:43:46.000Z",
  "title": "A group theoretic proof of Frobenius' theorem",
  "authors": [
    "Liguo He",
    "Congru Xu"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Let G be a Frobenius group with the Frobenius kernel N. Applying character theory, G. Frobenius proved that N was a normal subgroup of G in the year 1901. This is a celebrated application of the character theory of finite groups. In the note, we give a character-free proof of this result, which is a well-known problem in the theory of finite groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-06T05:43:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15",
      "20Dxx"
    ],
    "keywords": [
      "group theoretic proof",
      "finite groups",
      "frobenius kernel",
      "normal subgroup",
      "applying character theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}