On the structure of some modules over generalized soluble groups

TL;DR

This paper investigates the structure of certain modules over generalized soluble groups, focusing on modules where quotients by centralizers are artinian-by-finite rank, revealing new structural properties.

Contribution

It introduces a new class of modules over generalized soluble groups and analyzes their properties when quotients by centralizers are artinian-by-finite rank.

Findings

Modules with artinian-by-finite rank quotients exhibit specific structural characteristics.

The study extends understanding of modules over generalized soluble groups.

Results may influence the classification of modules in group representation theory.

Abstract

Let R be a ring and G a group. An R-module A is said to be artinian-by-(finite rank) if TorR(A) is artinian and A/TorR(A) has finite R-rank. The authors study ZG-modules A such that A/CA(H) is artinian-by-(finite rank) (as a Z-module) for every proper subgroup H.