On the primitive representations of finitely generated metabelian groups of finite rank over a field of non-zero characteristic

Abstract

We consider some conditions for imprimitivity of irreducible representations of a metebelian group $G$ of finite rank over a field $k$. We shoved that in the case where $char\; k = p > 0$ these conditions strongly depend on existence of infinite $p$-sections in $G$.

Keywords

• primitive representations
• metabelian groups
• rank of groups