ON ONE CLASS OF MODULES OVER GROUP RINGS WITH FINITENESS RESTRICTIONS

The author studies the RG-module A such that R is an associative ring, a group G has innite section p-rank (or innite 0-rank), CG(A) = 1, and for every proper subgroup H of infinite section p-rank (or innite 0-rank respectively) the quotient module A=CA(H) is a finite R-module. It is proved that if the group G under consideration is locally soluble then G is a soluble group and A=CA(G) is a finite R-module.