11.51 (1990)

Are there (large, non-trivial) classes $\mathfrak{X}$ of torsion-free abelian groups such that for $A, C \in \mathfrak{X}$ the group $\operatorname{Ext}(C, A)$ is torsion-free? It is a fact (E. L. Lady, A. Mader, J. Algebra, 140 (1991), 36–64) that two groups of such a class are nearly isomorphic if and only if they have equal $p$-ranks for all $p$.