Zn-graded Lie rings

Thompson proved that every finite group with a fixed point free automorphism of prime order is nilpotent and G. Higman proved that the nilpotency class is bounded in terms of the prime alone. Kreknin and Kostrikin produced the first explicit bound by reducing to the problem of bounding the nilpotency class of a Zp-graded Lie ring L with L0=0. Meixner later improved this bound. A step in the proof of Kreknin and Kostrikin is to bound the derived length of Zn-graded Lie rings L with L0=0. In this paper we improve these bounds.