{
  "id": "1112.5880",
  "version": "v1",
  "published": "2011-12-26T18:52:08.000Z",
  "updated": "2011-12-26T18:52:08.000Z",
  "title": "Centralizers of coprime automorphisms of finite groups",
  "authors": [
    "Cristina Acciarri",
    "Pavel Shumyatsky"
  ],
  "comment": "10 pages, submitted",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $A$ be an elementary abelian group of order $p^{k}$ with $k\\geq 3$ acting on a finite $p'$-group $G$. The following results are proved. If $\\gamma_{k-2}(C_{G}(a))$ is nilpotent of class at most $c$ for any $a\\in A^{#}$, then $\\gamma_{k-2}(G)$ is nilpotent and has $\\{c,k,p\\}$-bounded nilpotency class. If, for some integer $d$ such that $2^{d}+2\\leq k$, the $d$th derived group of $C_{G}(a)$ is nilpotent of class at most $c$ for any $a\\in A^{#}$, then the $d$th derived group $G^{(d)}$ is nilpotent and has $\\{c,k,p\\}$-bounded nilpotency class. Earlier this was known only in the case where $k\\leq 4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-26T18:52:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D45",
      "20F40"
    ],
    "keywords": [
      "finite groups",
      "coprime automorphisms",
      "th derived group",
      "bounded nilpotency class",
      "centralizers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.5880A"
    }
  }
}