# More Abelian groups with free duals

### George M. Bergman

University of California, Berkeley, USA

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## 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.

## Cite this article

George M. Bergman, More Abelian groups with free duals. Port. Math. 69 (2012), no. 1, pp. 69–84

DOI 10.4171/PM/1905