On Artinian Modules Over Group Rings DG where D is a Dedekind Domain
by
Igor Subbotin
National University, Los Angeles, California
Coauthors: Leonid A. Kurdachenko (Dnepropetrovsk University, Ukraine)

The problem of the investigation of artinian and noetherian modules over different rings is one of the oldest in algebra. An important side of this problem is the describing of the G-structure of an artinian FG-module. For example, the study of metabilian (even metanilpotent) groups with the minimal condition on normal subgroups required the investigation of artinian modules over Chernikov groups. Descriptions of these modules were obtained by B. Hartley and D. McDougall.  Artinian modules over abelian groups of finite rank were studied by L.A. Kurdachenko. The structure of some artinian modules over polycyclic groups were considered by I.M. Musson and S. Donkin. The study of modules over locally finite groups has its own specific character.  Here is a possibility to use some tools of the finite group theory and the representation theory. These possibilities arise more often if the group has many finite normal subgroups.  Hyperfinite groups (the groups possessing an ascending series of normal subgroups with finite factors) have this particular property and it allows us to obtain some constructive results about their structure.   

Date received: February 7, 1999