The pseudorational rank of an abelian group

We study finite-rank torsion-free abelian groups and quotient divisible mixed groups. We consider the pseudorational rank, a new invariant for finite-rank torsion-free groups which was introduced by A. A. Fomin, and establish its connection with the usual rank. We find a condition for existence of a homomorphism from one quotient divisible group into the other.