  If G and H are finitely generated, residually nilpotent metabelian groups, H
is termed para-G if there is a homomorphism of G into H which induces an
isomorphism between the corresponding terms of their lower central quotient
groups. We prove that this is an equivalence relation. It is a much coarser
relation than isomorphism, our ultimate concern. It turns out that many of the
groups in a given equivalence class share various properties including finite
presentability. There are examples, such as the lamplighter group, where an
equivalence class consists of a single isomorphism class and others where this
is not the case. We give several examples where we solve the Isomorphism
Problem. We prove also that the sequence of torsion-free ranks of the lower
central quotients of a finitely generated metabelian group is computable. In a
future paper we plan on proving that there is an algorithm to compute the
numerator and denominator of the rational Poincar\'e series of a finitely
generated metabelian group and will carry out this computation in a number of
examples, which may shed a tiny bit of light on the Isomorphism Problem. Our
proofs use localization, class field theory and some constructive commutative
algebra.
