{
  "id": "2002.10571",
  "version": "v1",
  "published": "2020-02-24T22:18:09.000Z",
  "updated": "2020-02-24T22:18:09.000Z",
  "title": "On Picent for blocks with normal defect group",
  "authors": [
    "Michael Livesey",
    "Claudio Marchi"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We prove that if $b$ is a block of a finite group with normal abelian defect group and inertial quotient a direct product of elementary abelian groups, then $\\operatorname{Picent}(b)$ is trivial. We also provide examples of blocks $b$ of finite groups with non-trivial $\\operatorname{Picent}(b)$. We even have examples with normal abelian defect group and abelian inertial quotient.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-24T22:18:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C20",
      "16D90"
    ],
    "keywords": [
      "normal defect group",
      "normal abelian defect group",
      "finite group",
      "abelian inertial quotient",
      "elementary abelian groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}