On separable $\widetilde{p}^{\alpha}$-bounded primary abelian groups

Abstract

The notion of $\ppb \a$-boundedness is used to study several topics in the theory of separable abelian $p$-groups, including the torsion product of torsion-complete groups, the generalized core class property, and in the context of the constructible universe, groups whose socles are essentially finitely indecomposable as valuated vector spaces.