{
  "id": "1410.5052",
  "version": "v1",
  "published": "2014-10-19T09:30:52.000Z",
  "updated": "2014-10-19T09:30:52.000Z",
  "title": "Subgroups of the upper-triangular matrix group with maximal derived length and a minimal number of generators",
  "authors": [
    "S. P. Glasby"
  ],
  "comment": "Differs from original publication because: an abstract is added, statement of main theorem is simplified, and retyped in LaTeX2e with hyperlinks. 9 pages",
  "journal": "Groups St Andrews 1997 in Bath, I, Edited by C.M. Campbell et al., London Mathematical Society Lecture Notes Series 260, Cambridge Univ. Press, (1999), 275--281",
  "categories": [
    "math.GR"
  ],
  "abstract": "The group U_n(F) of all nxn unipotent upper-triangular matrices over F has derived length d := Ceiling(log_2 (n)), equivalently 2^{d-1} < n <= 2^d. We prove that U_n(F) has a 3-generated subgroup of derived length d, and it has a 2-generated subgroup of derived length d if and only if (21/32)* 2^d < n <= 2^d.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-19T09:30:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D15"
    ],
    "keywords": [
      "upper-triangular matrix group",
      "maximal derived length",
      "minimal number",
      "nxn unipotent upper-triangular matrices",
      "generators"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}