{
  "id": "2006.11810",
  "version": "v1",
  "published": "2020-06-21T14:37:21.000Z",
  "updated": "2020-06-21T14:37:21.000Z",
  "title": "Profinite genus of fundamental groups of compact flat manifolds with holonomy group of prime order",
  "authors": [
    "Genildo de Jesus Nery"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "In this article we calculate the profinite genus of the fundamental group of a $n$-dimensional compact flat manifold $X$ with holonomy group of prime order. As consequence, we prove that if $n\\leq 21$, then $X$ is determined among all $n$-dimensional compact flat manifolds by the profinite completion of its fundamental group. Furthermore, we characterize the isomorphism class of profinite completion of the fundamental group of $X$ in terms of the representation genus of its holonomy group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-21T14:37:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fundamental group",
      "holonomy group",
      "prime order",
      "profinite genus",
      "dimensional compact flat manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}