On a Theorem of Stelzer for Some Classes of Mixed Groups

Abstract

We identify some classes \(\mathcal {C}\) of mixed groups such that if \(G\in \mathcal {C}\) has the cancellation property then the Walk-endomorphism ring of G has the unit lifting property. In particular, if G is a self-small group of torsion-free rank at most 4 with the cancellation property then it has a decomposition \(G=F\oplus H\) such that F is free and the Walk-endomorphism ring of H has the unit lifting property.