On composition factors in modules over some group rings

Authors

MARTYN RUSSELL DIXON
LEONID ANDREEVICH KURDACHENKO
IGOR YAKOV SUBBOTIN

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.

DOI

10.3906/mat-1908-65

Keywords

FC-hypercentral, module, FG-composition series, simple FG-module, quasifinite module, just infinite dimensional module

First Page

2806

Last Page

2817

Recommended Citation

DIXON, M. R, KURDACHENKO, L. A, & SUBBOTIN, I. Y (2019). On composition factors in modules over some group rings. Turkish Journal of Mathematics 43 (6): 2806-2817. https://doi.org/10.3906/mat-1908-65