On modules over group rings of soluble groups with commutative ring of scalars

Abstract

The author studies an RG-module A such that R is a commutative ring, A/CA(G) is not a Noetherian R-module, CG(A)=1, G is a soluble group. The system of all subgroups H≤G, for which the quotient modules A/CA(H) are not Noetherian R-modules, satisfies the maximal condition. This condition is called the condition max−nnd. The structure of the group G is described.