Maltsev bases for partially commutative nilpotent groups

TL;DR

This paper constructs a Maltsev basis for partially commutative nilpotent groups, providing a canonical form for elements, which advances understanding of their algebraic structure.

Contribution

It introduces a method to define a Maltsev basis in partially commutative nilpotent groups, enabling canonical forms for group elements.

Findings

Established a Maltsev basis for these groups

Provided a canonical form for elements

Enhanced algebraic understanding of 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 $F(X; \Gamma; \mathfrak N_m).$