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

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