On Triangularizability of a Group of Operators

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 ${mathcal{G}=mathcal{H}veemathcal{K}}$ , where ${mathcal{H}}$ is a normal subgroup consisting of singleton spectrum operators and ${mathcal{K}}$ is a triangularizable subgroup, then ${mathcal{G}}$ is triangularizable.