Basic Subgroups and Freeness, a counterexample

by Blass and Shelah. [BsSh:910]
Models, Modules and Abelian Groups, in Memory A.L.S. Corner, 2008
We construct a non-free but aleph_1-separable, torsion-free abelian group G with a pure free subgroup B such that all subgroups of G disjoint from B are free and such that G/B is divisible. This answers a question of Irwin and shows that a theorem of Blass and Irwin cannot be strengthened so as to give an exact analog for torsion-free groups of a result proved for p-groups by Benabdallah and Irwin.

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