On composition factors in modules over some group rings | Zendy

Martyn R. Dixon | Zendy; Leonid A. Kurdachenko | Zendy; Igor Ya. Subbotin | Zendy

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On composition factors in modules over some group rings

Author(s) -

Martyn R. Dixon,

Leonid A. Kurdachenko,

Igor Ya. Subbotin

Publication year - 2019

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1908-65

Subject(s) - dimension (graph theory) , composition (language) , mathematics , quotient , group (periodic table) , pure mathematics , finite group , factor (programming language) , combinatorics , algebra over a field , discrete mathematics , computer science , physics , philosophy , linguistics , programming language , quantum mechanics

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.

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