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 |
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Lugansk National Taras Shevchenko University
2018
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| 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| _version_ | 1856543334898597888 |
|---|---|
| author | Artemovych, Orest D. |
| author_facet | Artemovych, Orest D. |
| author_sort | Artemovych, Orest D. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-05-17T07:50:53Z |
| description | 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. |
| first_indexed | 2026-02-08T08:01:35Z |
| format | Article |
| id | admjournalluguniveduua-article-1170 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T08:01:35Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-11702018-05-17T07:50:53Z On subgroups of finite exponent in groups Artemovych, Orest D. locally finite group, finitely generated group, exponent, group of Heineken-Mohamed type 20F50, 20F26, 20E26 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. Lugansk National Taras Shevchenko University 2018-05-17 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1170 Algebra and Discrete Mathematics; Vol 19, No 1 (2015) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1170/659 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | locally finite group finitely generated group exponent group of Heineken-Mohamed type 20F50 20F26 20E26 Artemovych, Orest D. On subgroups of finite exponent in groups |
| title | On subgroups of finite exponent in groups |
| title_full | On subgroups of finite exponent in groups |
| title_fullStr | On subgroups of finite exponent in groups |
| title_full_unstemmed | On subgroups of finite exponent in groups |
| title_short | On subgroups of finite exponent in groups |
| title_sort | on subgroups of finite exponent in groups |
| topic | locally finite group finitely generated group exponent group of Heineken-Mohamed type 20F50 20F26 20E26 |
| topic_facet | locally finite group finitely generated group exponent group of Heineken-Mohamed type 20F50 20F26 20E26 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1170 |
| work_keys_str_mv | AT artemovychorestd onsubgroupsoffiniteexponentingroups |