2019
Том 71
№ 5

# On modules over group rings of nilpotent groups

Dashkova O. Yu.

Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 1, pp 13-23.

Citation Example: Dashkova O. Yu. On modules over group rings of nilpotent groups // Ukr. Mat. Zh. - 2012. - 64, № 1. - pp. 13-23.

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