Basic Subgroups and Freeness, A Counterexample
Logic
2007-11-21 v1 Group Theory
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.
Cite
@article{arxiv.0711.3031,
title = {Basic Subgroups and Freeness, A Counterexample},
author = {Andreas Blass and Saharon Shelah},
journal= {arXiv preprint arXiv:0711.3031},
year = {2007}
}