On extensions of bounded subgroups in Abelian groups

S. S. Gabriyelyan

On extensions of bounded subgroups in Abelian groups

S. S. Gabriyelyan

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

It is well-known that every bounded Abelian group is a direct sum of finite cyclic subgroups. We characterize those non-trivial bounded subgroups H of an infinite Abelian group G, for which there is an infinite subgroup G₀ of G containing H such that G₀ has a special decomposition into a direct sum which takes into account the properties of G, and which induces a natural decomposition of H into a direct sum of finite subgroups.

Original language	American English
Pages (from-to)	175-188
Number of pages	14
Journal	Commentationes Mathematicae Universitatis Carolinae
Volume	55
Issue number	2
State	Published - 1 Jan 2014

Keywords

Abelian group
Bounded group
Simple extension

All Science Journal Classification (ASJC) codes

General Mathematics

Cite this

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AB - It is well-known that every bounded Abelian group is a direct sum of finite cyclic subgroups. We characterize those non-trivial bounded subgroups H of an infinite Abelian group G, for which there is an infinite subgroup G0 of G containing H such that G0 has a special decomposition into a direct sum which takes into account the properties of G, and which induces a natural decomposition of H into a direct sum of finite subgroups.

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KW - Bounded group

KW - Simple extension

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On extensions of bounded subgroups in Abelian groups

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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