Geodesic
Structure of coordinate groups for algebraic sets in partially commutative nilpotent groups
Algebra i logika, Tome 48 (2009) no. 3, pp. 378-399

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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.
Keywords: partially commutative class two nilpotent $\mathbb Q$-group, geometric equivalence, algebraic set. 
@article{AL_2009_48_3_a3,
     author = {A. A. Mishchenko},
     title = {Structure of coordinate groups for algebraic sets in partially commutative nilpotent groups},
     journal = {Algebra i logika},
     pages = {378--399},
     publisher = {mathdoc},
     volume = {48},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2009_48_3_a3/}
}
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A. A. Mishchenko. Structure of coordinate groups for algebraic sets in partially commutative nilpotent groups. Algebra i logika, Tome 48 (2009) no. 3, pp. 378-399. http://geodesic.mathdoc.fr/item/AL_2009_48_3_a3/