{
  "id": "1809.10332",
  "version": "v1",
  "published": "2018-09-27T03:34:59.000Z",
  "updated": "2018-09-27T03:34:59.000Z",
  "title": "Commensurability growths of algebraic groups",
  "authors": [
    "Khalid Bou-Rabee",
    "Tasho Kaletha",
    "Daniel Studenmund"
  ],
  "comment": "9 pages",
  "categories": [
    "math.GR",
    "math.RT"
  ],
  "abstract": "Fixing a subgroup $\\Gamma$ in a group $G$, the full commensurability growth function assigns to each $n$ the cardinality of the set of subgroups $\\Delta$ of $G$ with $[\\Gamma: \\Gamma \\cap \\Delta][\\Delta : \\Gamma \\cap \\Delta] \\leq n$. For pairs $\\Gamma \\leq G$, where $G$ is a Chevalley group scheme defined over $\\mathbb{Z}$ and $\\Gamma$ is an arithmetic lattice in $G$, we give precise estimates for the full commensurability growth, relating it to subgroup growth and a computable invariant that depends only on $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-27T03:34:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E26",
      "20G05",
      "20G20",
      "20G25"
    ],
    "keywords": [
      "algebraic groups",
      "full commensurability growth function assigns",
      "chevalley group scheme",
      "subgroup growth",
      "precise estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}