{
  "id": "1505.06293",
  "version": "v1",
  "published": "2015-05-23T08:46:22.000Z",
  "updated": "2015-05-23T08:46:22.000Z",
  "title": "On $K_p$-series and varieties generated by wreath products of $p$-groups",
  "authors": [
    "Vahagn H. Mikaelian"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $A$ be a nilpotent $p$-groups of finite exponent, and $B$ be an abelian $p$-groups of finite exponent. Then the wreath product $A {\\rm Wr} B$ generates the variety ${\\rm var}(A) {\\rm var}(B)$ if and only if the group $B$ contains a subgroup isomorphic to the direct product $C_{p^v}^\\infty$ of at least countably many copies of the cyclic group $C_{p^v}$ of order $p^v = \\exp{(B)}$. The obtained theorem continues our previous study of cases when ${\\rm var}(A {\\rm Wr} B ) = {\\rm var}(A){\\rm var}(B)$ holds for some other classes of groups $A$ and $B$ (abelian groups, finite groups, etc.).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-23T08:46:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E22",
      "20E10",
      "20K01",
      "20K25",
      "20D15"
    ],
    "keywords": [
      "wreath product",
      "finite exponent",
      "abelian groups",
      "theorem continues"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150506293M"
    }
  }
}