On Triangularizability of a Group of Operators

Abstract

Let ${\mathcal{G}}$ be a group of invertible linear transformations on a finite-dimensional vector space over an algebraically closed field. We show that if ${\mathcal{G}=\mathcal{H}\vee\mathcal{K}}$, where ${\mathcal{H}}$ is a normal subgroup consisting of singleton spectrum operators and ${\mathcal{K}}$ is a triangularizable subgroup, then ${\mathcal{G}}$ is triangularizable.