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Modules over group rings of groups with restrictions on the system of all proper subgroups | ||
| International Journal of Group Theory | ||
| مقاله 3، دوره 4، شماره 4، اسفند 2015، صفحه 43-48 اصل مقاله (189.59 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2015.5504 | ||
| نویسنده | ||
| Olga Dashkova* | ||
| Professor of the Branch of Moscow state university in Sevastopol | ||
| چکیده | ||
| We consider the class $\mathfrak M$ of $\bf R$--modules where $\bf R$ is an associative ring. Let $A$ be a module over a group ring $\bf R$$G$, $G$ be a group and let $\mathfrak L(G)$ be the set of all proper subgroups of $G$. We suppose that if $H \in \mathfrak L(G)$ then $A/C_{A}(H)$ belongs to $\mathfrak M$. We investigate an $\bf R$$G$--module $A$ such that $G \not = G'$, $C_{G}(A) = 1$. We study the cases: 1) $\mathfrak M$ is the class of all artinian $\bf R$--modules, $\bf R$ is either the ring of integers or the ring of $p$--adic integers; 2) $\mathfrak M$ is the class of all finite $\bf R$--modules, $\bf R$ is an associative ring; 3) $\mathfrak M$ is the class of all finite $\bf R$--modules, $\bf R$$=F$ is a finite field. | ||
| کلیدواژهها | ||
| group ring؛ linear group؛ module | ||
| مراجع | ||
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