More Abelian groups with free duals

TL;DR

This paper constructs a subgroup of Z^ω with a free abelian dual of continuum rank, addressing a question about the possible sizes of dual groups of subgroups.

Contribution

It provides a specific example of a subgroup with a large free dual and discusses the potential for even larger duals within Z^ω.

Findings

Constructed a subgroup of Z^ω with a free dual of size 2^{ℵ_0}.

Discussed the possibility of larger free duals in Z^ω.

Explored classes of subgroups with free duals.

Abstract

In answer to a question of A. Blass, J. Irwin and G. Schlitt, a subgroup G of the additive group Z^{\omega} is constructed whose dual, Hom(G,Z), is free abelian of rank 2^{\aleph_0}. The question of whether Z^{\omega} has subgroups whose duals are free of still larger rank is discussed, and some further classes of subgroups of Z^{\omega} are noted.