Quotient Divisible Groups of Rank 2

In the paper, representations of torsion-free Abelian groups of rank $$2$$ using torsion-free groups of rank $$1$$ are studied. Necessary and sufficient conditions are found under which a group given by such a representation is quotient divisible. A criterion is obtained for two $$p$$ -minimal quotient divisible torsion-free groups of rank $$2$$ to be isomorphic to each other. An example is constructed showing that two such groups can be embedded in each other but be nonisomorphic. A series of properties of fundamental systems of elements of quotient divisible groups of arbitrary finite rank is established.