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

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