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In answer to a question of A. Blass, J. Irwin and G. Schlitt, a subgroup of the additive group is constructed whose dual, Hom, is free abelian of rank The question of whether has subgroups whose duals are free of still higher rank is discussed, and some further classes of subgroups of are noted.
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George M. Bergman, More Abelian groups with free duals. Port. Math. 69 (2012), no. 1, pp. 69–84DOI 10.4171/PM/1905