Maltsev bases for partially commutative nilpotent groups

Abstract

We construct an ordered set of commutators in a partially commutative nilpotent group $F(X;\Gamma ;{\mathfrak{N}}_m)$. This set allows us to define a canonical form for each element of $F(X;\Gamma ;{\mathfrak{N}}_m)$. Namely, we construct a Maltsev basis for the group $F(X;\Gamma ;{\mathfrak{N}}_m).$