{
  "id": "1107.2590",
  "version": "v2",
  "published": "2011-07-13T16:29:05.000Z",
  "updated": "2013-05-17T14:16:47.000Z",
  "title": "Subdirect products of groups and the n-(n+1)-(n+2) Conjecture",
  "authors": [
    "Benno Kuckuck"
  ],
  "comment": "32 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "We analyse the subgroup structure of direct products of groups. Earlier work on this topic has revealed that higher finiteness properties play a crucial role in determining which groups appear as subgroups of direct products of free groups or limit groups. Here, we seek to relate the finiteness properties of a subgroup to the way it is embedded in the ambient product. To this end we formulate a conjecture on finiteness properties of fibre products of groups. We present different approaches to this conjecture, proving a general result on finite generation of homology groups of fibre products and, for certain special cases, results on the stronger finiteness properties F_n and FP_n.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-17T14:16:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20J05",
      "20E22",
      "20E07"
    ],
    "keywords": [
      "subdirect products",
      "conjecture",
      "fibre products",
      "higher finiteness properties play",
      "stronger finiteness properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.2590K"
    }
  }
}