This book highlights important developments on artinian modules over group rings of generalized nilpotent groups. Along with traditional topics such as direct decompositions of artinian modules, criteria of complementability for some important modules, and criteria of semisimplicity of artinian modules, it also focuses on recent advanced results on these matters. The theory of modules over groups has its own specific character that plays an imperative role here and, for example, allows a significant generalization of the classical Maschke Theorem on some classes of infinite groups. Conversely, it leads to establishing direct decompositions of artinian modules related to important natural formations, which, in turn, find very efficient applications in infinite groups.

First book focussing on artinian modules While usually the investigation of a corresponding ring structure precedes the study of a module over this ring, the book implements module properties through the artinian condition Includes supplementary material: sn.pub/extras

Inhalt
Modules with chain conditions.- Ranks of groups.- Some generalized nilpotent groups.- Artinian modules and the socle.- Reduction to subgroups of finite index.- Modules over Dedekind domains.- The Kovacs-Newman theorem.- Hartley's classes of modules.- The injectivity of some simple modules.- Direct decompositions in artinian modules.- On the countability of artinian modules over FC-hypercentral groups.- Artinian modules over periodic abelian groups.- Nearly injective modules.- Artinian modules over abelian groups of finite section rank.- The injective envelopes of simple modules over group rings.- Quasifinite modules.- Some applications: splitting over the locally nilpotent residual.