The classification of certain classes of torsion free Abelian groups

Let jy denote the class of torsion free Abelian groups of finite rank. It is shown that for Ae JZf, there is a quotient divisible subgroup QD(A) such that A/QD(A) is a reduced torsion group. Furthermore, QD(A) and AIQD(A) are unique up to quasi-isomorphism. Let & denote the subclass of Ssf of groups A such that for almost all primes p, the p-primary component of A/QD(A) is the direct sum of Tp(A) isomorphic cyclic groups where r p (A) denotes the p-rank of A. The groups in & are classified up to quasi-isomorphism, which generalizes the Beaumont-Pierce classification of quotient divisible groups.