{
  "id": "2006.11173",
  "version": "v1",
  "published": "2020-06-19T15:02:24.000Z",
  "updated": "2020-06-19T15:02:24.000Z",
  "title": "Donovan's conjecture and extensions by the centralizer of a defect group",
  "authors": [
    "Charles W. Eaton",
    "Michael Livesey"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We consider Donovan's conjecture in the context of blocks of groups $G$ with defect group $D$ and normal subgroups $N \\lhd G$ such that $G=C_D(D\\cap N)N$, extending similar results for blocks with abelian defect groups. As an application we show that Donovan's conjecture holds for blocks with defect groups of the form $Q_8 \\times C_{2^n}$ or $Q_8 \\times Q_8$ defined over a discrete valuation ring.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-19T15:02:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C20"
    ],
    "keywords": [
      "extensions",
      "centralizer",
      "abelian defect groups",
      "donovans conjecture holds",
      "extending similar results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}