k-Primitivity and images of primitive elements

Abstract

Communicated by I. P. ShestakovLet Fn be a free Lie algebra of finite rank n, n ≥ 2. We give another proof of the following criterion which is proven by Mikhalev and Zolotykh, using the idea of k-primitivity: An endomorphism of Fn preserving primitivity of elements is an automorphism.