{
  "id": "1801.01977",
  "version": "v1",
  "published": "2018-01-06T06:51:30.000Z",
  "updated": "2018-01-06T06:51:30.000Z",
  "title": "On varieties of groups generated by wreath products of abelian groups",
  "authors": [
    "Vahagn H. Mikaelian"
  ],
  "doi": "10.1090/conm/273",
  "categories": [
    "math.GR"
  ],
  "abstract": "Generalizing results of Higman and Houghton on varieties generated by wreath products of finite cycles, we prove that the (direct or cartesian) wreath product of arbitrary abelian groups $A$ and $B$ generates the product variety $var (A) \\cdot var (B)$ if and only if one of the groups $A$ and $B$ is not of finite exponent, or if $A$ and $B$ are of finite exponents $m$ and $n$ respectively and for all primes $p$ dividing both $m$ and $n$, the factors $B[p^k]/B[p^{k-1}]$ are infinite, where $B[s]=\\langle b\\in B|\\,b^{s}=1 \\rangle$ and where $p^k$ is the highest power of $p$ dividing $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-06T06:51:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E22",
      "20E10",
      "20K01",
      "20K25"
    ],
    "keywords": [
      "wreath product",
      "finite exponent",
      "arbitrary abelian groups",
      "product variety",
      "finite cycles"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}