When is a discrete bounded subgroup of an LCA group necessarily a topological direct summand? (Q2706984)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | When is a discrete bounded subgroup of an LCA group necessarily a topological direct summand? |
scientific article |
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28 March 2001
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locally compact abelian group
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pure subgroup
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topologically pure subgroup
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discrete bounded group
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When is a discrete bounded subgroup of an LCA group necessarily a topological direct summand? (English)
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The concepts of pure subgroup and topologically pure subgroup are introduced and utilised in answering the question posed in the name of the paper. In addition, it is shown how every nontrivial discrete bounded group can be embedded, as the torsion part, in some nonsplitting LCA group. Finally, the splitting LCA groups whose torsion part is discrete are characterized.
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