{
  "id": "math/0405122",
  "version": "v3",
  "published": "2004-05-07T16:06:45.000Z",
  "updated": "2005-01-23T06:09:57.000Z",
  "title": "Counting homomorphisms onto finite solvable groups",
  "authors": [
    "Daniel Matei",
    "Alexander I. Suciu"
  ],
  "comment": "30 pages; accepted for publication in the Journal of Algebra",
  "journal": "Journal of Algebra 286 (2005), 161-186",
  "doi": "10.1016/j.jalgebra.2005.01.009",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We present a method for computing the number of epimorphisms from a finitely-presented group G to a finite solvable group \\Gamma, which generalizes a formula of G\\\"aschutz. Key to this approach are the degree 1 and 2 cohomology groups of G, with certain twisted coefficients. As an application, we count low-index subgroups of G. We also investigate the finite solvable quotients of the Baumslag-Solitar groups, the Baumslag parafree groups, and the Artin braid groups.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-01-23T06:09:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20J05",
      "20F16",
      "20E07",
      "20F36",
      "57M05"
    ],
    "keywords": [
      "finite solvable group",
      "counting homomorphisms",
      "artin braid groups",
      "baumslag parafree groups",
      "count low-index subgroups"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5122M"
    }
  }
}