JournalspmVol. 69, No. 1pp. 69–84

More Abelian groups with free duals

  • George M. Bergman

    University of California, Berkeley, USA
More Abelian groups with free duals cover
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In answer to a question of A. Blass, J. Irwin and G. Schlitt, a subgroup GG of the additive group Zω\mathbb{Z}^\omega is constructed whose dual, Hom(G,Z)(G,\mathbb{Z}), is free abelian of rank 20.2^{\aleph_0}. The question of whether Zω\mathbb{Z}^\omega has subgroups whose duals are free of still higher rank is discussed, and some further classes of subgroups of Zω\mathbb{Z}^\omega are noted.

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

DOI 10.4171/PM/1905