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Countable extensions of torsion Abelian groups. (English) Zbl 1114.20030

Suppose that \(A\) is a torsion countable Abelian extension of an Abelian group \(G\), and \(\mathbb{K}\) is a certain class of Abelian groups. The work is devoted to the problem when \(G\in\mathbb{K}\) implies that \(A\in\mathbb{K}\). The author solves the problem when \(\mathbb{K}\) represents the class of torsion \(\Sigma\)-groups, \(\sigma\)-summable \(p\)-groups, summable \(p\)-groups of countable length, torsion \(C_\lambda\)-groups, and \(p^{\omega+k}\)-projective \(p\)-groups.
Reviewer: David Kruml (Brno)

MSC:

20K10 Torsion groups, primary groups and generalized primary groups
20K35 Extensions of abelian groups
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