Equations in one variable over two-step nilpotent groups and chains of centralizers
Ivan M. Buchinskiy · Herald of Omsk University · 2024
In the article we prove the equivalence of the concepts of equationally Noetherianity of a torsion-free two-step nilpotent group and the existence in it of an infinite chain of strictly decreasing centralizers and present the idea of a two-way connection between equationally Noetherian partially commutative two-step nilpotent groups and equationally Noetherian graphs with loops.