Basic Subgroups and Freeness, A Counterexample

2007/11/19 by Blass, Andreas, Shelah, Saharon
#FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)

paper · doi:10.48550/arxiv.0711.3031

Abstract

We construct a non-free but aleph₁-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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