{
  "id": "1501.05670",
  "version": "v1",
  "published": "2015-01-22T22:02:07.000Z",
  "updated": "2015-01-22T22:02:07.000Z",
  "title": "On profinite groups with Engel-like conditions",
  "authors": [
    "Raimundo Bastos",
    "Pavel Shumyatsky"
  ],
  "journal": "Journal of Algebra, Volume 427, 1 April 2015, Pages 215-225",
  "doi": "10.1016/j.jalgebra.2015.01.002",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a profinite group in which for every element $x\\in G$ there exists a natural number $q=q(x)$ such that $x^q$ is Engel. We show that $G$ is locally virtually nilpotent. Further, let $p$ be a prime and $G$ a finitely generated profinite group in which for every $\\gamma_k$-value $x\\in G$ there exists a natural $p$-power $q=q(x)$ such that $x^q$ is Engel. We show that $\\gamma_k(G)$ is locally virtually nilpotent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-22T22:02:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E18",
      "20F45"
    ],
    "keywords": [
      "engel-like conditions",
      "locally virtually nilpotent",
      "natural number",
      "finitely generated profinite group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150105670B"
    }
  }
}