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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| Datum: | 2018 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
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| Schlagworte: | |
| Online Zugang: | 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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Algebra and Discrete Mathematics| Zusammenfassung: | 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. |
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