Direct decompositions of Artinian modules over hypercyclic groups

Let G be a hypercyclic group and A be an Artianian G-module. A class of simple G-modules is defined and it is proved that there exists a direct decomposition A=C B, where C is a G-submodule, each G-composition factor of which belongs to the class , and B is a G-submodule that does not have G-composition factors belonging to .Deceased.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, Nos. 7 and 8, pp. 930–934, July–August, 1991.