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 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 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.