Strongly homogeneous torsion free abelian groups of finite rank

An abelian group is strongly homogeneous if for any two pure rank 1 subgroups there is an automorphism sending one onto the other. Finite rank torsion free strongly homogeneous groups are characterized as the tensor product of certain subrings of algebraic number fields with finite direct sums of isomorphic subgroups of $Q$, the additive group of rationals. If $G$ is a finite direct sum of finite rank torsion free strongly homogeneous groups, then any two decompositions of $G$ into a direct sum of indecomposable subgroups are equivalent.