{
  "id": "1411.5389",
  "version": "v1",
  "published": "2014-11-19T21:36:33.000Z",
  "updated": "2014-11-19T21:36:33.000Z",
  "title": "Upper bounds on the number of conjugacy classes in unitriangular groups",
  "authors": [
    "Andrew Soffer"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We provide a new upper bound on the number of conjugacy classes in the group $U_n(q)$ of unitriangular matrices over a finite field. Higman originally introduced this problem and gave the first upper bound as a means of bounding the number of $p$-groups of a given order, though the question itself is of independent interest. Our tools also allow us to compute an upper bound for every term in the lower central series of $U_n(q)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-19T21:36:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conjugacy classes",
      "unitriangular groups",
      "first upper bound",
      "lower central series",
      "finite field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.5389S"
    }
  }
}