On modules over group rings of locally soluble groups for a ring of p -adic integers

Abstract

The author studies the Zp∞G-module A such that Zp∞ is a ring of p-adic integers, a group G is locally soluble, the quotient module A/CA(G) is not Artinian Zp∞-module, and the system of all subgroups H≤G for which the quotient modules A/CA(H) are not Artinian Zp∞-modules satisfies the minimal condition on subgroups. It is proved that the group G under consideration is soluble and some its properties are obtained.