Basic subgroups and freeness, a counterexample [chapter]

Rüdiger Göbel, Brendan Goldsmith
2008 Models, Modules and Abelian Groups  
We construct a non-free but ℵ1-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.
doi:10.1515/9783110203035.63 fatcat:djyviqkywrevblbslpxqdbdf3y