{
  "id": "1610.07397",
  "version": "v1",
  "published": "2016-10-24T13:14:34.000Z",
  "updated": "2016-10-24T13:14:34.000Z",
  "title": "Brauer relations for finite groups in the ring of semisimplified modular representations",
  "authors": [
    "Matthew Spencer"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We study the kernel of the map between the Burnside ring of a finite group $G$ and the Grothendieck ring of $\\mathbb{F}_p[G]$ modules for a prime $p$, which takes a $G$-set to its associated permutation module. We are able to give a classification of the primitive quotient of the kernel; the kernel for $G$ modulo elements coming from the kernel for proper subquotients of $G$, for all finite groups. In the soluble case we are able to identify exactly which groups have primitive elements in the kernel and we give generators for the primitive quotient.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-24T13:14:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite group",
      "semisimplified modular representations",
      "brauer relations",
      "primitive quotient",
      "associated permutation module"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}