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 \( {\mathfrak L} \) nm (G) be the system of all subgroups H ≤ G such that the quotient modules A/C A (H) are not minimax R-modules. We investigate an 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 satisfying these conditions is a minimax group.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 1, pp. 14–23, January, 2012.
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Dashkova, O.Y. On modules over group rings of nilpotent groups. Ukr Math J 64, 13–23 (2012). https://doi.org/10.1007/s11253-012-0626-0
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DOI: https://doi.org/10.1007/s11253-012-0626-0