{
  "id": "1709.05068",
  "version": "v1",
  "published": "2017-09-15T06:23:27.000Z",
  "updated": "2017-09-15T06:23:27.000Z",
  "title": "On a minimal counterexample to Brauer's $k(B)$-conjecture",
  "authors": [
    "Gunter Malle"
  ],
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "We study Brauer's long-standing $k(B)$-conjecture on the number of characters in $p$-blocks for finite quasi-simple groups and show that their blocks do not occur as a minimal counterexample for $p\\ge5$. For $p=3$ we obtain that the principal 3-blocks do not provide minimal counterexamples. We also determine the precise number of irreducible characters in unipotent blocks of classical groups for odd primes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-15T06:23:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15",
      "20C33"
    ],
    "keywords": [
      "minimal counterexample",
      "conjecture",
      "finite quasi-simple groups",
      "odd primes",
      "precise number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}