More Abelian groups with free duals

Abstract

In answer to a question of A. Blass, J. Irwin and G. Schlitt, a subgroup $G$ of the additive group ${\mathbb{Z}}^{\omega }$ is constructed whose dual, Hom$(G,\mathbb{Z})$, is free abelian of rank $2^{{\aleph }_0}.$ The question of whether ${\mathbb{Z}}^{\omega }$ has subgroups whose duals are free of still higher rank is discussed, and some further classes of subgroups of ${\mathbb{Z}}^{\omega }$ are noted.