TY - JOUR AU - O. Yu. Dashkova PY - 2012/01/25 Y2 - 2024/03/29 TI - On modules over group rings of nilpotent groups JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 64 IS - 1 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2552 AB - We study an $\mathbf{R}G$-module $A$, where $\mathbf{R}$ is a ring, $A/C_A(G)$ is not a minimax $\mathbf{R}$-module, $C_A(G) = 1$, and $G$ is a nilpotent group. Let $\mathfrak{L}_{nm}(G)$ be the system of all subgroups $H \leq G$ such that the quotient modules $A/C_A(G)$ are not minimax $\mathbf{R}$-modules. We investigate a $\mathbf{R}G$ - 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. ER -