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ON TWO PROBLEMS CONCERNING EXTENSION GROUPS OF ABELIAN GROUPS

П. А. Крылов

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Abstract

This paper deals with the extension group of an abelian group by an abelian group . In §1 the problem of how the groups , are related to one another if for any group is completely solved for a torsion-free group of finite rank (Theorem 1.7).Also studied are conditions under which the group is torsion-free. Theorem 2.5 describes the torsion-free groups , of finite rank with the property, more general than the situation in [13], that both and are torsion-free.Bibliography: 20 titles.

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What this paper is about

This paper deals with the extension group of an abelian group by an abelian group . In §1 the problem of how the groups , are related to one another if for any group is completely solved for a torsion-free group of finite rank (Theorem 1.7).Also studied are conditions under which the group is torsion-free. Theorem 2.5 describes the torsion-free groups , of finite rank with the property, more general than the situation in [13], that both and are torsion-free.Bibliography: 20 titles.

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Available abstract

This paper deals with the extension group of an abelian group by an abelian group . In §1 the problem of how the groups , are related to one another if for any group is completely solved for a torsion-free group of finite rank (Theorem 1.7).Also studied are conditions under which the group is torsion-free. Theorem 2.5 describes the torsion-free groups , of finite rank with the property, more general than the situation in [13], that both and are torsion-free.Bibliography: 20 titles.

Key concepts: Mathematics, Extension (predicate logic), Abelian group, Pure mathematics, Elementary abelian group, Algebra over a field, Rank of an abelian group, Torsion subgroup

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