Structure of coordinate groups for algebraic sets in partially commutative nilpotent groups

The results obtained deal in algebraic geometry over partially commutative class two nilpotent $\mathbb Q$-groups, where $\mathbb Q$ is a field of rationals. It is proved that two arbitrary non-Abelian partially commutative class two nilpotent $\mathbb Q$-groups are geometrically equivalent. A necessary and sufficient condition of being universally geometrically equivalent is specified for two partially commutative class two nilpotent $\mathbb Q$-groups. Algebraic sets for systems of equations in one variable, as well as for some special systems in several variables, are described.