{
  "id": "1808.05354",
  "version": "v1",
  "published": "2018-08-16T06:13:37.000Z",
  "updated": "2018-08-16T06:13:37.000Z",
  "title": "The lower $p$-central series of a free profinite group and the shuffle algebra",
  "authors": [
    "Ido Efrat"
  ],
  "categories": [
    "math.NT",
    "math.KT",
    "math.RA"
  ],
  "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 lower $p$-central filtration of $S$. For $p>n$, we give a combinatorial description of $H^2(S/S^{(n,p)},\\mathbb{Z}/p)$ in terms of the Shuffle algebra on $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-16T06:13:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12G05",
      "68R15",
      "12F10",
      "12E30"
    ],
    "keywords": [
      "free profinite group",
      "shuffle algebra",
      "central series",
      "central filtration",
      "prime number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}