On primitive representations of minimax nilpotent groups (Q1810170)

Let \(F\) be a field and let \(G\) be a group. A simple \(FG\)-module \(A\) is called imprimitive if \(G\) has a proper subgroup \(H\) and \(A\) contains an \(FH\)-submodule \(B\) such that \(A=B\otimes_{FH}FG\). If \(A\) is not imprimitive, then it is called primitive. The main result of this paper is the following Theorem. Let \(G\) be a nilpotent of class two minimax group, \(F\) a finitely generated field of characteristic zero. If there exists a simple primitive \(FG\)-module \(A\), then \(G/C_G(A)\) is finitely generated.