{
  "id": "1511.04333",
  "version": "v1",
  "published": "2015-11-13T16:04:54.000Z",
  "updated": "2015-11-13T16:04:54.000Z",
  "title": "Subgroup Growth in Some Profinite Chevalley Groups",
  "authors": [
    "Inna Capdeboscq",
    "Karina Kirkina",
    "Dmitriy Rumynin"
  ],
  "comment": "10 pages",
  "categories": [
    "math.GR",
    "math.RA",
    "math.RT"
  ],
  "abstract": "In this article we improve the known uniform bound for subgroup growth of Chevalley groups over $\\mathbf{G}(\\mathbb{F}_p[[t]])$. We introduce a new parameter, the ridgeline number $v(\\mathbf{G})$, and give new bounds for the subgroup growth of $\\mathbf{G}(\\mathbb{F}_p[[t]])$ expressed through $v(\\mathbf{G})$. We achieve this by deriving a new estimate for the codimension of $[U,V]$ where $U$ and $V$ are vector subspaces in the Lie algebra of $\\mathbf{G}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-13T16:04:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E07",
      "17B45",
      "17B70"
    ],
    "keywords": [
      "subgroup growth",
      "profinite chevalley groups",
      "uniform bound",
      "ridgeline number",
      "vector subspaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151104333C"
    }
  }
}