On the structure of groups admitting faithful modules with certain conditions of primitivity

A.V. Tushev

doi:10.15421/242307

On the structure of groups admitting faithful modules with certain conditions of primitivity

A.V. Tushev (Oles Honchar Dnipro National University), https://orcid.org/0000-0001-5219-1986

Abstract

In the paper we study structure of soluble-by-finite groups of finite torsion-free rank which admit faithful modules with conditions of primitivity. In particular, we prove that under some additional conditions if an infinite finitely generated linear group $$$G$$$ of finite rank admits a fully primitive fully faithful module then $$$G$$$ has infinite $$$FC$$$-centre.

Keywords

nilpotent groups; minimax groups; group rings; induced modules

MSC 2020

16S34; 20C07; 11R27

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References

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