{
  "id": "1702.05440",
  "version": "v1",
  "published": "2017-02-17T17:13:57.000Z",
  "updated": "2017-02-17T17:13:57.000Z",
  "title": "Simple modules in the Auslander-Reiten quiver of principal blocks with abelian defect groups",
  "authors": [
    "Shigeo Koshitani",
    "Caroline Lassueur"
  ],
  "comment": "19pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Given an odd prime $p$, we investigate the position of simple modules in the stable Auslander-Reiten quiver of the principal block of a finite group with non-cyclic abelian Sylow $p$-subgroups. In particular, we prove a reduction to finite simple groups. In the case that the characteristic is $3$, we prove that simple modules in the principal block all lie at the end of their components",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-17T17:13:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C20",
      "16G70"
    ],
    "keywords": [
      "simple modules",
      "principal block",
      "abelian defect groups",
      "non-cyclic abelian sylow",
      "finite simple groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}