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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| 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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oai:ojs.admjournal.luguniv.edu.ua: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 |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-05-17T07:50:53Z |
| collection |
OJS |
| language |
English |
| topic |
locally finite group finitely generated group exponent group of Heineken-Mohamed type 20F50 20F26 20E26 |
| 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 |
| topic_facet |
locally finite group finitely generated group exponent group of Heineken-Mohamed type 20F50 20F26 20E26 |
| format |
Article |
| author |
Artemovych, Orest D. |
| author_facet |
Artemovych, Orest D. |
| author_sort |
Artemovych, Orest D. |
| title |
On subgroups of finite exponent in groups |
| title_short |
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_sort |
on subgroups of finite exponent in groups |
| 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1170 |
| work_keys_str_mv |
AT artemovychorestd onsubgroupsoffiniteexponentingroups |
| first_indexed |
2025-07-17T10:36:06Z |
| last_indexed |
2025-07-17T10:36:06Z |
| _version_ |
1837890081246937088 |