On subdirect sums of Abelian torsion-free groups of rank 1

In this paper, we study torsion\df free Abelian groups of rank 2, which are subdirect sums of two divisible rational groups, with the inducing group $\mathbb{Q}/\mathbb{Z}$. The class of special groups is defined and investigated. It is shown that there is a one-to-one correspondence between the set of all special groups and the multiplicative group of unity elements of the ring of universal numbers.