The lower central series of the free partially commutative group

Abstract

This paper is devoted to the study of the lower central series of the free partially commutative group F(A, θ{symbol}) in connection with the associated free partially commutative Lie algebra. Using a convenient Magnus transformation, we show that the quotients of the lower central series of F(A, θ{symbol}) are free abelian groups and that F(A, θ{symbol}) can be fully ordered. © 1992 Springer-Verlag.