{
  "id": "2203.00313",
  "version": "v1",
  "published": "2022-03-01T09:41:52.000Z",
  "updated": "2022-03-01T09:41:52.000Z",
  "title": "Lower defect groups and vertices of simple modules",
  "authors": [
    "Akihiko Hida",
    "Masao Kiyota"
  ],
  "comment": "10 pages",
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "We compare lower defect groups associated with $p$-regular classes and vertices of simple modules for a block of a finite group algebra. We show that lower defect groups are contained in vertices of simple modules after suitable reordering. Moreover, for a block of principal type, we show that a $p$-regular lower defect group which contains a vertex of simple module is a defect group of the block.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-01T09:41:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C20"
    ],
    "keywords": [
      "simple module",
      "regular lower defect group",
      "finite group algebra",
      "principal type",
      "regular classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}