{
  "id": "2003.08903",
  "version": "v1",
  "published": "2020-03-19T17:01:43.000Z",
  "updated": "2020-03-19T17:01:43.000Z",
  "title": "The $p$-Zassenhaus Filtration of a Free Profinite Group and Shuffle Relations",
  "authors": [
    "Ido Efrat"
  ],
  "categories": [
    "math.NT",
    "math.GR"
  ],
  "abstract": "For a prime number $p$ and a free profinite group $S$ on the basis $X$, let $S_{(n,p)}$, $n=1,2,\\ldots,$ be the $p$-Zassenhaus filtration of $S$. For $p>n$, we give a word-combinatorial description of the cohomology group $H^2(S/S_{(n,p)},\\mathbb{Z}/p)$ in terms of the shuffle algebra on $X$. We give a natural linear basis for this cohomology group, which is constructed by means of unitriangular representations arising from Lyndon words.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-19T17:01:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12G05",
      "68R15",
      "12F10",
      "12E30"
    ],
    "keywords": [
      "free profinite group",
      "zassenhaus filtration",
      "shuffle relations",
      "cohomology group",
      "natural linear basis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}