On subgroups of finite exponent in groups
We investigate properties of groups with subgroups of finite exponent and prove that a non-perfect group \(G\) of infinite exponent with all proper subgroups of finite exponent has the following properties:\((1)\) \(G\) is an indecomposable \(p\)-group,\((2)\) if the derived subgroup \(G'\...
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| Datum: | 2018 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
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| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1170 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Zusammenfassung: | We investigate properties of groups with subgroups of finite exponent and prove that a non-perfect group \(G\) of infinite exponent with all proper subgroups of finite exponent has the following properties:\((1)\) \(G\) is an indecomposable \(p\)-group,\((2)\) if the derived subgroup \(G'\) is non-perfect, then \(G/G''\) is a group of Heineken-Mohamed type.We also prove that a non-perfect indecomposable group \(G\) with the non-perfect locally nilpotent derived subgroup \(G'\) is a locally finite \(p\)-group. |
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