Absolutely closed nil-2 groups

Abstract.

Using the description of dominions in the variety of nilpotent groups of class at most two, we give a characterization of which groups are absolutely closed in this variety. We use the general result to derive an easier characterization for some subclasses; e.g., an abelian group G is absolutely closed in N ₂ if and only if G/pG is cyclic for every prime number p.