Locally soluble AFA-groups
Let $A$ be an $\mathbf{R}G$-module, where $\mathbf{R}$ is a ring, $G$ is a locally solvable group, $C_G (A) = 1$, and each proper subgroup $H$ of $G$ for which $A/C_A(H)$ is not an Artinian $\mathbf{R}$-module is finitely generated. It is proved that a locally solvable group $G$ that satisfies thes...
Збережено в:
| Дата: | 2013 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2013
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/2431 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | Let $A$ be an $\mathbf{R}G$-module, where $\mathbf{R}$ is a ring, $G$ is a locally solvable group, $C_G (A) = 1$, and each proper subgroup $H$ of $G$ for which $A/C_A(H)$
is not an Artinian $\mathbf{R}$-module is finitely generated. It is proved that a locally solvable group $G$ that satisfies these conditions is hyperabelian
if R is a Dedekind ring. We describe the structure of $G$ in the case where $G$ is a finitely generated solvable group, $A/C_A(H)$ is not an Artinian $\mathbf{R}$-module and $\mathbf{R}$ is a Dedekind ring. |
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