On one class of modules over integer group rings of locally solvable groups

Abstract

We study a ZG-module A in the case where the group G is locally solvable and satisfies the condition min-naz and its cocentralizer in A is not an Artinian Z-module. We prove that the group G is solvable under the conditions indicated above. The structure of the group G is studied in detail in the case where this group is not a Chernikov group.

Modules over group rings of locally soluble groups with a certain condition of minimality

“…It is investigated an RG-module A such that the system L nad .G/ satisfies the minimal condition as an ordered set, G is a locally soluble group, C G .A/ D 1. The analogous problem for the ring of integers R was investigated in [3].…”