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.
FC-hypercentral, module, FG-composition series, simple FG-module, quasifinite module, just infinite dimensional module
DIXON, MARTYN RUSSELL; KURDACHENKO, LEONID ANDREEVICH; and SUBBOTIN, IGOR YAKOV
"On composition factors in modules over some group rings,"
Turkish Journal of Mathematics: Vol. 43:
6, Article 12.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss6/12