{
  "id": "1611.01313",
  "version": "v1",
  "published": "2016-11-04T10:34:19.000Z",
  "updated": "2016-11-04T10:34:19.000Z",
  "title": "Narain Gupta's three normal subgroup problem and group homology",
  "authors": [
    "Roman Mikhailov",
    "Inder Bir S. Passi"
  ],
  "comment": "20 pages",
  "categories": [
    "math.GR",
    "math.KT"
  ],
  "abstract": "This paper is about application of various homological methods to classical problems in the theory of group rings. It is shown that the third homology of groups plays a key role in Narain Gupta's three normal subgroup problem. For a free group $F$ and its normal subgroups $R,\\,S,\\,T,$ and the corresponding ideals in the integral group ring $\\mathbb Z[F]$, ${\\bf r}=(R-1)\\mathbb Z[F],\\ {\\bf s}=(S-1)\\mathbb Z[F],\\ {\\bf t}=(T-1)\\mathbb Z[F],$ a complete description of the normal subgroup $F\\cap (1+{\\bf rst})$ is given, provided $R\\subseteq T$ and the third and the fourth homology groups of $R/R\\cap S$ are torsion groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-04T10:34:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "normal subgroup problem",
      "narain guptas",
      "group homology",
      "fourth homology groups",
      "torsion groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}