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In answer to a question of A. Blass, J. Irwin and G. Schlitt, a subgroup G of the additive group ℤω is constructed whose dual, Hom(G, ℤ), is free abelian of rank 2א0. The question of whether ℤω has subgroups whose duals are free of still higher rank is discussed, and some further classes of subgroups of ℤω are noted.
