On modules over group rings of nilpotent groups

We study an R G-module A; where R is a ring, A/C (A) (G) is not a minimax R-module, C (G) (A) = 1; and G is a nilpotent group. Let (nm) (G) be the system of all subgroups H a parts per thousand currency signaEuro parts per thousand G such that the quotient modules A/C (A) (H) are not minimax R-modules. We investigate an R G-module A such that (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 satisfying these conditions is a minimax group.