Dashkova, O. (2015). Modules over group rings of groups with restrictions on the system of all proper subgroups. International Journal of Group Theory, 4(4), 43-48. doi: 10.22108/ijgt.2015.5504

Olga Dashkova. "Modules over group rings of groups with restrictions on the system of all proper subgroups". International Journal of Group Theory, 4, 4, 2015, 43-48. doi: 10.22108/ijgt.2015.5504

Dashkova, O. (2015). 'Modules over group rings of groups with restrictions on the system of all proper subgroups', International Journal of Group Theory, 4(4), pp. 43-48. doi: 10.22108/ijgt.2015.5504

Dashkova, O. Modules over group rings of groups with restrictions on the system of all proper subgroups. International Journal of Group Theory, 2015; 4(4): 43-48. doi: 10.22108/ijgt.2015.5504

Modules over group rings of groups with restrictions on the system of all proper subgroups

^{}Professor of the Branch of Moscow state university in Sevastopol

Abstract

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.

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