Abstract

Suppose that a finite group G admits a Frobenius group FH of automorphisms with kernel F and complement H such that the fixed-point subgroup of F is trivial, i.e., CG(F) = 1, and the orders of G and H are coprime. It is proved that the nilpotent length of G is equal to the nilpotent length of CG(H) and the Fitting series of the fixed-point subgroup CG(H) coincides with a series obtained by taking intersections of CG(H) with the Fitting series of G. © 2011 Springer Science+Business Media, Inc.