{
  "id": "1311.0138",
  "version": "v1",
  "published": "2013-11-01T10:44:30.000Z",
  "updated": "2013-11-01T10:44:30.000Z",
  "title": "On the length of the shortest non-trivial element in the derived and the lower central series",
  "authors": [
    "Abdelrhman Elkasapy",
    "Andreas Thom"
  ],
  "comment": "10 pages, no figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "We provide upper and lower bounds on the length of the shortest non-trivial element in the derived series and lower central series in the free group on two generators. The techniques are used to provide new estimates on the nilpotent residual finiteness growth and on almost laws for compact groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-01T10:44:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E05"
    ],
    "keywords": [
      "shortest non-trivial element",
      "lower central series",
      "nilpotent residual finiteness growth",
      "free group",
      "lower bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.0138E"
    }
  }
}