Derived Subgroups of Fixed Points in Profinite Groups
  The main result of this paper is the following theorem. Let q be a prime, A an elementary abelian group of order q^3. Suppose that A acts as a coprime group of automorphisms on a profinite group G in such a manner that C_G(a)' is periodic for each nontrivial element a in A. Then G' is locally finite. 
C. Acciarri, A. de Souza Lima, P. Shumyatsky
math.GR