The lower central series of the free partially commutative group

This paper is devoted to the study of the lower central series of the free partially commutative groupF(A, ϑ) 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 ofF(A, ϑ) are free abelian groups and thatF(A, ϑ) can be fully ordered.