{
  "id": "1102.4267",
  "version": "v3",
  "published": "2011-02-21T16:11:19.000Z",
  "updated": "2011-05-25T06:13:25.000Z",
  "title": "Blocks with defect group D_{2^n} x C_{2^m}",
  "authors": [
    "Benjamin Sambale"
  ],
  "comment": "8 pages, shorter proofs, some typos corrected",
  "categories": [
    "math.RT"
  ],
  "abstract": "We determine the numerical invariants of blocks with defect group D_{2^n}\\times C_{2^m}, where D_{2^n} denotes a dihedral group of order 2^n and C_{2^m} denotes a cyclic group of order 2^m. This generalizes Brauer's results for m=0. As a consequence, we prove Brauer's k(B)-conjecture, Olsson's conjecture (and more generally Eaton's conjecture), Brauer's height zero conjecture, the Alperin-McKay conjecture, Alperin's weight conjecture and Robinson's ordinary weight conjecture for these blocks. Moreover, we show that the gluing problem has a unique solution in this case.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-05-25T06:13:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15",
      "20C20"
    ],
    "keywords": [
      "defect group",
      "robinsons ordinary weight conjecture",
      "brauers height zero conjecture",
      "alperins weight conjecture",
      "generalizes brauers results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.4267S"
    }
  }
}