On composition factors in modules over some group rings

Abstract

The aim of this paper is to prove the following result: Let G be an FC-hypercentral group and let Ahave a finite FG-composition series. Then A contains two FG-submodules B,C such that A = B ⊕ C, where eachFG-composition factor of B has finite F -dimension and each FG-composition factor of C has infinite F -dimension.This has consequences for FG-modules whose proper submodules all have finite F -dimension and for those FG-moduleswhose proper quotients all have finite F -dimension.