On modules over group rings of nilpotent groups - Dashkova, O. Yu. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
We study an $RG$-module $A$, where $R$ is a ring, $A/C_A(G)$ is not a minimax $R$-module, $C_A(G) = 1$, and $G$ is a nilpotent group. Let $\mathfrak{L}_{nm}(G)$ be the system of all subgroups $H ≤ G$ such that the quotient modules $A/C_A(G)$ are not minimax $R$-modules. We investigate a $RG$ - module $A$ such that $\mathfrak{L}_{nm}(G)$ satisfies either the weak minimal condition or the weak maximal condition as an ordered set. It is proved that a nilpotent group $G$ that satisfies these conditions is a minimax group.