{
  "id": "1704.03433",
  "version": "v1",
  "published": "2017-04-11T17:26:46.000Z",
  "updated": "2017-04-11T17:26:46.000Z",
  "title": "On the Table of Marks of a Direct Product of Finite Groups",
  "authors": [
    "Brendan Masterson",
    "Götz Pfeiffer"
  ],
  "comment": "27 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "We present a method for computing the table of marks of a direct product of finite groups. In contrast to the character table of a direct product of two finite groups, its table of marks is not simply the Kronecker product of the tables of marks of the two groups. Based on a decomposition of the inclusion order on the subgroup lattice of a direct product as a relation product of three smaller partial orders, we describe the table of marks of the direct product essentially as a matrix product of three class incidence matrices. Each of these matrices is in turn described as a sparse block diagonal matrix. As an application, we use a variant of this matrix product to construct a ghost ring and a mark homomorphism for the rational double Burnside algebra of the symmetric group~$S_3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-11T17:26:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "direct product",
      "finite groups",
      "sparse block diagonal matrix",
      "matrix product",
      "rational double burnside algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}