{
  "id": "1105.4977",
  "version": "v1",
  "published": "2011-05-25T09:42:08.000Z",
  "updated": "2011-05-25T09:42:08.000Z",
  "title": "Blocks with defect group D_{2^n} * C_{2^m}",
  "authors": [
    "Benjamin Sambale"
  ],
  "comment": "10 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We determine the numerical invariants of blocks with defect group D_{2^n} * C_{2^m} = Q_{2^n} * C_{2^m} (central product), where n > 2 and m > 1. 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": "v1",
      "updated": "2011-05-25T09:42:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15",
      "20C20"
    ],
    "keywords": [
      "defect group",
      "robinsons ordinary weight conjecture",
      "brauers height zero conjecture",
      "alperins weight conjecture",
      "central product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.4977S"
    }
  }
}