{
  "id": "math/0607703",
  "version": "v1",
  "published": "2006-07-27T11:31:26.000Z",
  "updated": "2006-07-27T11:31:26.000Z",
  "title": "The functor of units of Burnside rings for p-groups",
  "authors": [
    "Serge Bouc"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "In this note I describe the structure of the biset functor $B^\\times$ sending a $p$-group $P$ to the group of units of its Burnside ring $B(P)$. In particular, I show that $B^\\times$ is a rational biset functor. It follows that if $P$ is a $p$-group, the structure of $B^\\times(P)$ can be read from a genetic basis of $P$: the group $B^\\times(P)$ is an elementary abelian 2-group of rank equal to the number isomorphism classes of rational irreducible representations of $P$ whose type is trivial, cyclic of order 2, or dihedral.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-07-27T11:31:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "19A22",
      "16U60"
    ],
    "keywords": [
      "burnside ring",
      "rational biset functor",
      "number isomorphism classes",
      "elementary abelian",
      "rational irreducible representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7703B"
    }
  }
}