{
  "id": "2008.02433",
  "version": "v1",
  "published": "2020-08-06T02:34:31.000Z",
  "updated": "2020-08-06T02:34:31.000Z",
  "title": "Groups in which the co-degrees of the irreducible characters are distinct",
  "authors": [
    "Mahdi Ebrahimi"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a finite group and let $\\rm{Irr}(G)$ be the set of all irreducible complex characters of $G$. For a character $\\chi \\in \\rm{Irr}(G)$, the number $\\rm{cod}(\\chi):=|G:\\rm{ker}\\chi|/\\chi(1)$ is called the co-degree of $\\chi$. The set of co-degrees of all irreducible characters of $G$ is denoted by $\\rm{cod}(G)$. In this paper, we show that for a non-trivial finite group $G$, $|\\rm{Irr}(G)|=|\\rm{cod}(G)|$ if and only if $G$ is isomorphic to the cyclic group $\\mathbb{Z}_2$ or the symmetric group $S_3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-06T02:34:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15",
      "05C25"
    ],
    "keywords": [
      "irreducible characters",
      "non-trivial finite group",
      "symmetric group",
      "irreducible complex characters",
      "cyclic group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}