On locally soluble \(\mathrm A \mathrm F \mathrm N\)-groups
Let \(A\) be an \({\mathbf{R}G}\)-module, where \(\bf R\) is a commutative ring, \(G\) is a locally soluble group, \(C_{G}(A)=1\), and each proper subgroup \(H\) of \(G\) for which \(A/C_{A}(H)\) is not a noetherian \(\bf R\)-module, is finitely generated. We describe the structure of a locally solu...
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/710 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| id |
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admjournalluguniveduua-article-7102018-04-04T09:58:22Z On locally soluble \(\mathrm A \mathrm F \mathrm N\)-groups Dashkova, Olga Yu. locally soluble group, noetherian module, group ring 20F19 Let \(A\) be an \({\mathbf{R}G}\)-module, where \(\bf R\) is a commutative ring, \(G\) is a locally soluble group, \(C_{G}(A)=1\), and each proper subgroup \(H\) of \(G\) for which \(A/C_{A}(H)\) is not a noetherian \(\bf R\)-module, is finitely generated. We describe the structure of a locally soluble group \(G\) with these conditions and the structure of \(G\) under consideration if \(G\) is a finitely generated soluble group and the quotient module \(A/C_{A}(G)\) is not a noetherian \(\bf R\)-module. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/710 Algebra and Discrete Mathematics; Vol 14, No 1 (2012) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/710/243 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-04-04T09:58:22Z |
| collection |
OJS |
| language |
English |
| topic |
locally soluble group noetherian module group ring 20F19 |
| spellingShingle |
locally soluble group noetherian module group ring 20F19 Dashkova, Olga Yu. On locally soluble \(\mathrm A \mathrm F \mathrm N\)-groups |
| topic_facet |
locally soluble group noetherian module group ring 20F19 |
| format |
Article |
| author |
Dashkova, Olga Yu. |
| author_facet |
Dashkova, Olga Yu. |
| author_sort |
Dashkova, Olga Yu. |
| title |
On locally soluble \(\mathrm A \mathrm F \mathrm N\)-groups |
| title_short |
On locally soluble \(\mathrm A \mathrm F \mathrm N\)-groups |
| title_full |
On locally soluble \(\mathrm A \mathrm F \mathrm N\)-groups |
| title_fullStr |
On locally soluble \(\mathrm A \mathrm F \mathrm N\)-groups |
| title_full_unstemmed |
On locally soluble \(\mathrm A \mathrm F \mathrm N\)-groups |
| title_sort |
on locally soluble \(\mathrm a \mathrm f \mathrm n\)-groups |
| description |
Let \(A\) be an \({\mathbf{R}G}\)-module, where \(\bf R\) is a commutative ring, \(G\) is a locally soluble group, \(C_{G}(A)=1\), and each proper subgroup \(H\) of \(G\) for which \(A/C_{A}(H)\) is not a noetherian \(\bf R\)-module, is finitely generated. We describe the structure of a locally soluble group \(G\) with these conditions and the structure of \(G\) under consideration if \(G\) is a finitely generated soluble group and the quotient module \(A/C_{A}(G)\) is not a noetherian \(\bf R\)-module. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/710 |
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AT dashkovaolgayu onlocallysolublemathrmamathrmfmathrmngroups |
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2025-12-02T15:43:13Z |
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2025-12-02T15:43:13Z |
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1850411783933657088 |