Large indecomposable roots of Ext (Q5931435)

The main theorem of this paper implies that for any \(\aleph_1\)-free Abelian group \(D\) there are arbitrarily large indecomposable groups \(G\) such that \(\text{Ext}(D,G)=0\). In more generality, the theorem applies to every \(D\) which is \(p\)-cotorsion-free, that is, \(D\) is reduced and torsion-free and there is no non-zero homomorphism from the \(p\)-adic completion of \(\mathbb{Z}\) to \(D\). Moreover, \(G\) can be constructed to be rigid, that is, the endomorphism ring of \(G\) is \(\mathbb{Z}\).NEWLINENEWLINENEWLINEThe proof uses a combination of Shelah's Black Box and a construction method due to the reviewer and the second author [Bull. Lond. Math. Soc. 33, No. 1, 41-51 (2001)].