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

Danchev, Peter

Arch. Math., Brno 41, No. 3, 265-272 (2005).

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

Keywords:

countable factor-groups; \(\Sigma\)-groups; summable groups; Abelian torsion groups; torsion Abelian extensions; totally projective \(p\)-groups