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Turkish Journal of Mathematics

DOI

10.3906/mat-1908-65

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.

First Page

2806

Last Page

2817

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Mathematics Commons

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