On composition factors in modules over some group rings

Authors : Martyn Russell Dixon, Leonid Andreevich Kurdachenko, Igor Yakov Subbotin

Pages : 2806-2817

View : 11 | Download : 9

Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :The aim of this paper is to prove the following result: Let G be an FC-hypercentral group and let A have a finite FG-composition series. Then A contains two FG-submodules B,C such that A = B ⊕ C, where each FG-composition factor of B has finite F -dimension and each FG-composition factor of C has infinite F -dimension. Thishasconsequencesfor FG-modules whose proper submodules all have finite F -dimensionandforthose FG-modules whose proper quotients all have finite F -dimension.
Keywords : FC-hypercentral, module, FG-composition series, simple FG-module, quasifinite module, just infinite dimensional module