{
  "id": "0809.2166",
  "version": "v3",
  "published": "2008-09-12T09:29:18.000Z",
  "updated": "2011-05-30T06:56:12.000Z",
  "title": "On the descending central sequence of absolute Galois groups",
  "authors": [
    "Ido Efrat",
    "Jan Minac"
  ],
  "comment": "We implemented the referee's comments. The paper will appear in The American Journal of Mathematics",
  "categories": [
    "math.NT",
    "math.KT"
  ],
  "abstract": "Let $p$ be an odd prime number and $F$ a field containing a primitive $p$th root of unity. We prove a new restriction on the group-theoretic structure of the absolute Galois group $G_F$ of $F$. Namely, the third subgroup $G_F^{(3)}$ in the descending $p$-central sequence of $G_F$ is the intersection of all open normal subgroups $N$ such that $G_F/N$ is 1, $\\mathbb{Z}/p^2$, or the modular group $M_{p^3}$ of order $p^3$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-05-30T06:56:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12F10",
      "12G05",
      "12E30"
    ],
    "keywords": [
      "absolute galois group",
      "descending central sequence",
      "odd prime number",
      "open normal subgroups",
      "modular group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.2166E"
    }
  }
}