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A simple proof for a theorem of Chase. (English) Zbl 0583.20042

The author gives a new proof of the following well-known Theorem of Chase: Assume \(2^{\aleph_ 0}<2^{\aleph_ 1}\). If G is a torsion- free group such that Ext(G,Z) is torsion, then G is strongly \(\aleph_ 1\)-free.
The idea of the proof is obvious for some one familiar with recent structure theorems of Ext, the solution of the Whitehead problem etc: Use the weak diamond (Devlin and Shelah) which follows from the set theoretic assumption. The smoothest way to prove Chase’s theorem is then by Baer’s factor systems.
Reviewer: R.Göbel

MSC:

20K20 Torsion-free groups, infinite rank
20K27 Subgroups of abelian groups
20K35 Extensions of abelian groups
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References:

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