{
  "id": "1102.4427",
  "version": "v1",
  "published": "2011-02-22T08:03:41.000Z",
  "updated": "2011-02-22T08:03:41.000Z",
  "title": "Simple exceptional groups of Lie type are determined by their character degrees",
  "authors": [
    "Hung P. Tong-Viet"
  ],
  "comment": "18 pages",
  "categories": [
    "math.GR",
    "math.RT"
  ],
  "abstract": "Let $G$ be a finite group. Denote by $\\textrm{Irr}(G)$ the set of all irreducible complex characters of $G.$ Let $\\textrm{cd}(G)=\\{\\chi(1)\\;|\\;\\chi\\in \\textrm{Irr}(G)\\}$ be the set of all irreducible complex character degrees of $G$ forgetting multiplicities, and let $\\textrm{X}_1(G)$ be the set of all irreducible complex character degrees of $G$ counting multiplicities. Let $H$ be any non-abelian simple exceptional group of Lie type. In this paper, we will show that if $S$ is a non-abelian simple group and $\\textrm{cd}(S)\\subseteq \\textrm{cd}(H)$ then $S$ must be isomorphic to $H.$ As a consequence, we show that if $G$ is a finite group with $\\textrm{X}_1(G)\\subseteq \\textrm{X}_1(H)$ then $G$ is isomorphic to $H.$ In particular, this implies that the simple exceptional groups of Lie type are uniquely determined by the structure of their complex group algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-22T08:03:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15"
    ],
    "keywords": [
      "lie type",
      "irreducible complex character degrees",
      "finite group",
      "non-abelian simple exceptional group",
      "complex group algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.4427T"
    }
  }
}