{
  "id": "math/0212366",
  "version": "v1",
  "published": "2002-12-29T03:59:58.000Z",
  "updated": "2002-12-29T03:59:58.000Z",
  "title": "Finiteness Properties of S-Arithmetic Groups - a Survey",
  "authors": [
    "Kai-Uwe Bux"
  ],
  "comment": "28 pages, 5 figures",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We give an overview about finiteness properties of soluble S-arithmetic groups. Both, the number field case and the function field case are covered. The main result is: If B is a Borel subgroup in a Chevalley group and R is an S-arithmetic ring, then the group B(R) has finiteness length |S|-1 in the function field case, and infinite finiteness length in the number field case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-12-29T03:59:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G30",
      "20F65"
    ],
    "keywords": [
      "finiteness properties",
      "function field case",
      "number field case",
      "infinite finiteness length",
      "soluble s-arithmetic groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....12366B"
    }
  }
}