{
  "id": "1712.08103",
  "version": "v1",
  "published": "2017-12-21T17:37:20.000Z",
  "updated": "2017-12-21T17:37:20.000Z",
  "title": "Nilpotent residual of fixed points",
  "authors": [
    "Emerson de Melo",
    "Aline de Souza Lima",
    "Pavel Shumyatsky"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $q$ be a prime and $A$ a finite $q$-group of exponent $q$ acting by automorphisms on a finite $q'$-group $G$. Assume that $A$ has order at least $q^3$. We show that if $\\gamma_{\\infty} (C_{G}(a))$ has order at most $m$ for any $a \\in A^{\\#}$, then the order of $\\gamma_{\\infty} (G)$ is bounded solely in terms of $m$ and $q$. If $\\gamma_{\\infty} (C_{G}(a))$ has rank at most $r$ for any $a \\in A^{\\#}$, then the rank of $\\gamma_{\\infty} (G)$ is bounded solely in terms of $r$ and $q$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-21T17:37:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nilpotent residual",
      "fixed points",
      "automorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}