{
  "id": "1809.07934",
  "version": "v1",
  "published": "2018-09-21T03:40:45.000Z",
  "updated": "2018-09-21T03:40:45.000Z",
  "title": "Residual dimension of nilpotent groups: correction to \"Effective separability of finitely generated nilpotent groups\"",
  "authors": [
    "Mark Pengitore"
  ],
  "comment": "28 Pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "The functions $\\text{F}_{G}(n)$ and $\\text{Conj}_{G}(n)$ measure the asymptotic behavior of residual finiteness and conjugacy separability for a finitely generated group $G$, respectively. In previous work, the author claimed a characterization for $\\text{F}_{G}(n)$ and lower asymptotic bounds for $\\text{Conj}_{G}(n)$ when $G$ is a finitely generated nilpotent group. However, a counterexample to the characterization of $\\text{F}_{G}(n)$ for finitely generated nilpotent groups was communicated to the author which also had consequences to the lower asymptotic bound provided for $\\text{Conj}_{G}(n)$. Subsequently, the statements of the asymptotic characterization of $\\text{F}_{G}(n)$ and the asymptotic lower bound for $\\text{Conj}_{G}(n)$ along with their proofs are incorrect. In this article, we provide correct lower asymptotic bounds for $\\text{F}_{G}(n)$ and asymptotic lower bounds for $\\text{Conj}_{G}(n)$ when $G$ is a finitely generated nilpotent group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-21T03:40:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F18"
    ],
    "keywords": [
      "finitely generated nilpotent group",
      "residual dimension",
      "effective separability",
      "asymptotic lower bound",
      "correction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}