{
  "id": "1501.05423",
  "version": "v1",
  "published": "2015-01-22T08:44:08.000Z",
  "updated": "2015-01-22T08:44:08.000Z",
  "title": "Varieties generated by wreath products of abelian and nilpotent groups",
  "authors": [
    "Vahagn H. Mikaelian"
  ],
  "comment": "The concise versions of this text will appear in Russian in 'Algebra i Logika' (L.S. Sobolev Mathematics Institute) and in English in 'Algebra and Logic' (Springer)",
  "doi": "10.13140/2.1.2300.9607",
  "categories": [
    "math.GR"
  ],
  "abstract": "We present a survey of our recent research on varieties, generated by wreath products of groups. In particular, the full classification of all cases, when the (cartesian or direct) wreath product of any abelian groups $A$ and $B$ generates the product variety $\\var{A} \\var{B}$, is given. The analog of this is given for sets of abelian groups. We also present new, unpublished research on cases when the similar question is considered for non-abelian, finite groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-22T08:44:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E22",
      "20E10",
      "20K01",
      "20K25"
    ],
    "keywords": [
      "wreath product",
      "nilpotent groups",
      "abelian groups",
      "product variety"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "ru",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150105423M"
    }
  }
}