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Characteristic properties of large subgroups in primary Abelian groups. (English) Zbl 1062.20059

The purpose of this paper is the study of relations between the structures of primary Abelian groups and their large subgroups. The results have the form “\(G\) belongs to the class of Abelian \(p\)-groups \(\mathcal K\) if and only if a fixed large subgroup \(L\) belongs to \(\mathcal K\)”. This is proved to hold for several classes of primary Abelian groups: summable, \(\sigma\)-summable, \(\Sigma\)-groups, \(p^{\omega+1}\)-projective.
Reviewer’s remark: Some similar results were already proved in the 70’s for the standard example of large subgroups \(L=p^nG\).

MSC:

20K10 Torsion groups, primary groups and generalized primary groups
20K27 Subgroups of abelian groups
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