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Torsion groups in cotorsion classes. (English) Zbl 1097.20042

For torsion-free Abelian groups \(G\) of arbitrary rank the author discusses the class \(\mathcal{TC}(G)\) of all torsion groups \(T\) satisfying \(\text{Ext}(G,T)=0\). This subclass consists of the torsion groups cogenerated by \(G\). The author investigates under which conditions on \(G\) there exists a subgroup \(\mathbb{Z}\subset R\subset\mathbb{Q}\) such that \(\mathcal{TC}(G)= \mathcal{TC}(R)\).

MSC:

20K35 Extensions of abelian groups
20K40 Homological and categorical methods for abelian groups
20K10 Torsion groups, primary groups and generalized primary groups
20K20 Torsion-free groups, infinite rank
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References:

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