{
  "id": "2203.11099",
  "version": "v1",
  "published": "2022-03-21T16:26:54.000Z",
  "updated": "2022-03-21T16:26:54.000Z",
  "title": "A quantitative Neumann lemma for finitely generated groups",
  "authors": [
    "Elia Gorokhovsky",
    "Nicolás Matte Bon",
    "Omer Tamuz"
  ],
  "comment": "8 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "We study the coset covering function $\\mathfrak{C}(r)$ of a finitely generated group: the number of cosets of infinite index subgroups needed to cover the ball of radius $r$. We show that $\\mathfrak{C}(r)$ is linear for virtually nilpotent groups, exponential for property (T) groups, and is of order at least $\\sqrt{r}$ for all groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-21T16:26:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finitely generated group",
      "quantitative neumann lemma",
      "infinite index subgroups",
      "coset covering function",
      "virtually nilpotent groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}