On a theorem of Stelzer for some classes of mixed groups

Abstract

We identify some classes C of mixed groups such that if G ∈ 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 ⊕ H such that F is free and the Walk-endomorphism ring of H has the unit lifting property.