{
  "id": "math/0611403",
  "version": "v3",
  "published": "2006-11-13T20:45:00.000Z",
  "updated": "2007-01-19T21:56:11.000Z",
  "title": "The generating hypothesis for the stable module category of a $p$-group",
  "authors": [
    "David J. Benson",
    "Sunil K. Chebolu",
    "J. Daniel Christensen",
    "Jan Minac"
  ],
  "comment": "6 pages, fixed minor typos, to appear in J. Algebra",
  "journal": "Journal of Algebra 310 (2007) 428-433",
  "categories": [
    "math.RT",
    "math.AT"
  ],
  "abstract": "Freyd's generating hypothesis, interpreted in the stable module category of a finite p-group G, is the statement that a map between finite-dimensional kG-modules factors through a projective if the induced map on Tate cohomology is trivial. We show that Freyd's generating hypothesis holds for a non-trivial finite p-group G if and only if G is either C_2 or C_3. We also give various conditions which are equivalent to the generating hypothesis.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-01-19T21:56:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C20",
      "20J06",
      "55P42"
    ],
    "keywords": [
      "stable module category",
      "non-trivial finite p-group",
      "finite-dimensional kg-modules factors",
      "freyds generating hypothesis holds"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11403B"
    }
  }
}