  To define the notion of a generic property of finite dimensional 2-step
nilpotent Lie algebras we use standard correspondence between such Lie algebras
and points of an appropriate algebraic variety, where a negligible set is one
contained in a proper Zariski-closed subset. We compute the maximal dimension
of an abelian subalgebra of a generic Lie algebra and give a sufficient
condition for a generic Lie algebra to admit no surjective homomorphism onto a
non-abelian Lie algebra of a given dimension. Also we consider analogous
questions for finitely generated torsion free nilpotent groups of class 2.
