{
  "id": "math/0507335",
  "version": "v2",
  "published": "2005-07-16T15:40:10.000Z",
  "updated": "2005-08-03T15:27:35.000Z",
  "title": "Induction of Characters and Finite $p$-Groups",
  "authors": [
    "Edith Adan-Bante"
  ],
  "comment": "11 pages, corrected typos",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a finite $p$-group, where $p$ is an odd prime number, $H$ be a subgroup of $G$ and $\\theta\\in \\Irr(H)$ be an irreducible character of $H$. Assume also that $|G:H|=p^2$. Then the character $\\theta^G$ of $ G$ induced by $\\theta$ is either a multiple of an irreducible character of $G$, or has at least $\\frac{p+1}{2}$ distinct irreducible constituents.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-08-03T15:27:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "odd prime number",
      "irreducible character",
      "distinct irreducible constituents"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7335A"
    }
  }
}