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Ukrainian Mathematical Journal

, Volume 64, Issue 1, pp 13–23 | Cite as

On modules over group rings of nilpotent groups

  • O. Yu. Dashkova
Article
  • 45 Downloads

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.

Keywords

Normal Subgroup Linear Group Nilpotent Group Quotient Group Abelian Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  • O. Yu. Dashkova
    • 1
  1. 1.Gonchar Dnepropetrovsk National UniversityDnepropetrovskUkraine

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