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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| Date: | 2018 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1170 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | 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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