On modules over group rings of locally soluble groups for a ring of \(p\)-adic integers
The author studies the \(\bf Z_{p^{\infty}}\)\(G\)-module \(A\) such that \(\bf Z_{p^{\infty}}\) is a ring of \(p\)-adic integers, a group \(G\) is locally soluble, the quotient module \(A/C_{A}(G)\) is not Artinian \(\bf Z_{p^{\infty}}\)-module, and the system of all subgroups \(H \leq G\) for whic...
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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/767 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-7672018-04-04T08:31:48Z On modules over group rings of locally soluble groups for a ring of \(p\)-adic integers Dashkova, O. Yu. Linear group, Artinian module, locally soluble group 20F19; 20H25 The author studies the \(\bf Z_{p^{\infty}}\)\(G\)-module \(A\) such that \(\bf Z_{p^{\infty}}\) is a ring of \(p\)-adic integers, a group \(G\) is locally soluble, the quotient module \(A/C_{A}(G)\) is not Artinian \(\bf Z_{p^{\infty}}\)-module, and the system of all subgroups \(H \leq G\) for which the quotient modules \(A/C_{A}(H)\) are not Artinian \(\bf Z_{p^{\infty}}\)-modules satisfies the minimal condition on subgroups. It is proved that the group \(G\) under consideration is soluble and some its properties are obtained. 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/767 Algebra and Discrete Mathematics; Vol 8, No 1 (2009) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/767/297 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-04-04T08:31:48Z |
| collection |
OJS |
| language |
English |
| topic |
Linear group Artinian module locally soluble group 20F19 20H25 |
| spellingShingle |
Linear group Artinian module locally soluble group 20F19 20H25 Dashkova, O. Yu. On modules over group rings of locally soluble groups for a ring of \(p\)-adic integers |
| topic_facet |
Linear group Artinian module locally soluble group 20F19 20H25 |
| format |
Article |
| author |
Dashkova, O. Yu. |
| author_facet |
Dashkova, O. Yu. |
| author_sort |
Dashkova, O. Yu. |
| title |
On modules over group rings of locally soluble groups for a ring of \(p\)-adic integers |
| title_short |
On modules over group rings of locally soluble groups for a ring of \(p\)-adic integers |
| title_full |
On modules over group rings of locally soluble groups for a ring of \(p\)-adic integers |
| title_fullStr |
On modules over group rings of locally soluble groups for a ring of \(p\)-adic integers |
| title_full_unstemmed |
On modules over group rings of locally soluble groups for a ring of \(p\)-adic integers |
| title_sort |
on modules over group rings of locally soluble groups for a ring of \(p\)-adic integers |
| description |
The author studies the \(\bf Z_{p^{\infty}}\)\(G\)-module \(A\) such that \(\bf Z_{p^{\infty}}\) is a ring of \(p\)-adic integers, a group \(G\) is locally soluble, the quotient module \(A/C_{A}(G)\) is not Artinian \(\bf Z_{p^{\infty}}\)-module, and the system of all subgroups \(H \leq G\) for which the quotient modules \(A/C_{A}(H)\) are not Artinian \(\bf Z_{p^{\infty}}\)-modules satisfies the minimal condition on subgroups. It is proved that the group \(G\) under consideration is soluble and some its properties are obtained. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/767 |
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AT dashkovaoyu onmodulesovergroupringsoflocallysolublegroupsforaringofpadicintegers |
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2025-07-17T10:35:44Z |
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2025-07-17T10:35:44Z |
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1837890058956308480 |