{
  "id": "0809.3046",
  "version": "v3",
  "published": "2008-09-18T01:17:17.000Z",
  "updated": "2009-03-25T19:00:16.000Z",
  "title": "Groups with the same cohomology as their pro-$p$ completions",
  "authors": [
    "Karl Lorensen"
  ],
  "comment": "The revisions in the second version pertain to the exposition: the proof of Prop. 1.1, in particular, now includes more details. The third version includes a proof that right-angled Artin groups are residually $p$-finite for every prime $p$",
  "journal": "J. Pure Appl. Algebra 214 (2010), 6-14",
  "categories": [
    "math.GR",
    "math.KT"
  ],
  "abstract": "For any prime $p$ and group $G$, denote the pro-$p$ completion of $G$ by $\\hat{G}^p$. Let $\\mathcal{C}$ be the class of all groups $G$ such that, for each natural number $n$ and prime number $p$, $H^n(\\hat{G^p},\\mathbb Z/p)\\cong H^n(G, \\mathbb Z/p)$, where $\\mathbb Z/p$ is viewed as a discrete, trivial $\\hat{G}^p$-module. In this article we identify certain kinds of groups that lie in $\\mathcal{C}$. In particular, we show that right-angled Artin groups are in $\\mathcal{C}$ and that this class also contains some special types of free products with amalgamation.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-03-25T19:00:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E18",
      "20E06",
      "20F36"
    ],
    "keywords": [
      "completion",
      "cohomology",
      "natural number",
      "free products",
      "right-angled artin groups"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.3046L"
    }
  }
}