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...
Збережено в:
| Дата: | 2018 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
|
| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/767 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | 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. |
|---|