When the group of extensions Ext\((A,B)\) is torsion free (Q1902830)

In Section 1 we obtain criteria for the group \(\text{Ext}(A,B)\) to be torsion free with arbitrary finite rank torsion free groups \(A\) and \(B\) (Theorem 1.1). Most simply these criteria are formulated for a \(p\)- irreducible group \(A\). In Section 2 for a finite-exact finite rank torsion free \(S\)-group \(A\) (see Definition 2.1) and an arbitrary torsion free group \(B\) it is clarified when \(\text{Ext}(A,B)\) will be a torsion free group (Theorem 2.1). We obtain some corollaries following from Theorem 2.1 as well.