Generalized cotorsion locally compact abelian groups (Q442632)
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scientific article; zbMATH DE number 6063120
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Generalized cotorsion locally compact abelian groups |
scientific article; zbMATH DE number 6063120 |
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Generalized cotorsion locally compact abelian groups (English)
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3 August 2012
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locally compact groups
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character group
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homological characteristics of groups
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cotorsion groups
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A discrete group \(A\) is called a cotorsion group iff \(Ext(Q,A)=0\), where \(Q\) is the additive group of rational numbers. (Here \(Ext(Q,A)=0\) is the group of all extensions of \(A\) by \(Q\).) Cotorsion groups play an important role in the theory of abelian groups. In the paper, a new class of locally compact abelian groups is constructed, which contains the class of cotorsion groups and its dual. The objects of this new class are called generalized cotorsion groups.NEWLINENEWLINE One of the main results of the paper: Theorem. The class of generalized cotorsion locally compact groups is closed under taking:NEWLINENEWLINE 1) extensions;NEWLINENEWLINE 2) finite direct sums;NEWLINENEWLINE 3) topologically direct summands;NEWLINENEWLINE 4) compact subgroups;NEWLINENEWLINE 5) discrete epimorphic images.NEWLINENEWLINE Some homological properties of generalized cotorsion groups are given.NEWLINENEWLINE Some results on the classification of generalized cotorsion groups are obtained.
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