Resumen de Frobenius groups as groups of automorphisms

N. Y. Makarenko, Pavel Shumyatsky

• We show that if is a double Frobenius group with ``upper'' complement of order such that is nilpotent of class , then is nilpotent of -bounded class. This solves a problem posed by Mazurov in the Kourovka Notebook. The proof is based on an analogous result on Lie rings: if a finite Frobenius group with kernel of prime order and complement of order acts on a Lie ring in such a way that and is nilpotent of class , then is nilpotent of -bounded class.