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CENTRALISER DIMENSION OF FREE PARTIALLY COMMUTATIVE NILPOTENT GROUPS OF CLASS 2

Abstract In an effort to extend the theory of algebraic geometry over groups beyond free groups, Duncan, Kazatchkov and Remeslennikov have studied the notion of centraliser dimension for free partially commutative groups. In this paper we consider the centraliser dimension of free partially commutative nilpotent groups of class 2, showing that a free partially commutative nilpotent group of class 2 with non-commutation graph Γ has the same centraliser dimension as the free partially commutative group represented by the non-commutation graph Γ.