On groups in which commutators are covered by finitely many cyclic subgroups. (Q934078)
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scientific article; zbMATH DE number 5304636
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On groups in which commutators are covered by finitely many cyclic subgroups. |
scientific article; zbMATH DE number 5304636 |
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On groups in which commutators are covered by finitely many cyclic subgroups. (English)
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29 July 2008
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It is natural to assume that if the set of all commutators of a group \(G\) is covered by finitely many subgroups, then the structure of the derived subgroup \([G,G]\) is determined in some way. The authors consider coverings of the set of commutators by finitely many cyclic subgroups. They obtain the following interesting result. Main Theorem. Let \(G\) be a group in which the set of all commutators can be covered by finitely many cyclic subgroups. Then \([G,G]\) is either finite or cyclic.
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coverings by cyclic subgroups
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commutators
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derived subgroup
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