# Sh:910

• Blass, A. R., & Shelah, S. (2008). Basic subgroups and freeness, a counterexample. In Models, modules and abelian groups, Walter de Gruyter, Berlin, pp. 63–73.
• Abstract:
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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Bib entry
@incollection{Sh:910,
author = {Blass, Andreas R. and Shelah, Saharon},
title = {{Basic subgroups and freeness, a counterexample}},
booktitle = {{Models, modules and abelian groups}},
year = {2008},
pages = {63--73},
publisher = {Walter de Gruyter, Berlin},
mrnumber = {2513227},
mrclass = {20K20 (03E05)},
doi = {10.1515/9783110203035.63},
note = {\href{https://arxiv.org/abs/0711.3031}{arXiv: 0711.3031}},
arxiv_number = {0711.3031}
}