  In this note we introduce the class of $\mathcal H$-groups (or Hall groups)
related to the class of $\mathcal B$-groups defined by Ph. Hall in 1950's.
Establishing some basic properties of Hall groups we use them to obtain results
concerning embeddings of abelian groups. In particular, we give an explicit
classification of all abelian groups that can occur as subgroups in
finitely-generated metabelian groups. Hall groups allow to give a negative
answer to the Baumslag's conjecture of 1990 on the cardinality of the set of
isomorphism classes for abelian subgroups in finitely generated metabelian
groups.
