{
  "id": "1902.08612",
  "version": "v1",
  "published": "2019-02-21T13:44:22.000Z",
  "updated": "2019-02-21T13:44:22.000Z",
  "title": "Engel-like conditions in fixed points of automorphisms of profinite groups",
  "authors": [
    "Cristina Acciarri",
    "Danilo Silveira"
  ],
  "comment": "14 pages. arXiv admin note: substantial text overlap with arXiv:1702.02899, arXiv:1707.06889, arXiv:1703.00988",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $q$ be a prime and $A$ an elementary abelian $q$-group acting as a coprime group of automorphisms on a profinite group $G$. We show that if $A$ is of order $q^2$ and some power of each element in $C_G(a)$ is Engel in $G$ for any $a\\in A^{\\#}$, then $G$ is locally virtually nilpotent. Assuming that $A$ is of order $q^3$ we prove that if some power of each element in $C_G(a)$ is Engel in $C_G(a)$ for any $a\\in A^{\\#}$, then $G$ is locally virtually nilpotent. Some analogues consequences of quantitative nature for finite groups are also obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-21T13:44:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "profinite group",
      "fixed points",
      "engel-like conditions",
      "automorphisms",
      "locally virtually nilpotent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}