Projective normality of quotient varieties modulo finite groups

In this note, we prove that for any finite dimensional vector space $V$ over an algebraically closed field $k$, and for any finite subgroup $G$ of $GL(V)$ which is either solvable or is generated by pseudo reflections such that the $\mathrm{\mid }G\mathrm{\mid }$ is a unit in $k$, the projective variety $\mathbb{P}(V)\mathrm{/}G$ is projectively normal with respect to the descent of $\mathcal{O}(1{)}^{\otimes \mathrm{\mid }G\mathrm{\mid }}$.