## 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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