Basic subgroups and a freeness criterion for torsion-free Abelian groups. (English) Zbl 0943.20052
Eklof, Paul C. (ed.) et al., Abelian groups and modules. Proceedings of the international conference in Dublin, Ireland, August 10-14, 1998. Basel: Birkhäuser. Trends in Mathematics. 247-255 (1999).
If \(G\) is a torsion-free Abelian group with a basic subgroup of infinite rank and if, for every basic subgroup \(B\) of \(G\) all \(B\)-high subgroups of \(G\) are free, then \(G\) is free. This is a confirmation of a conjecture of the second named author. There are a number of derived consequences of this result.
For the entire collection see [Zbl 0921.00018].
For the entire collection see [Zbl 0921.00018].
Reviewer: Radoslav M.Dimitrić (Berkeley)
