Let $G$ be a finite group of order $n$. Let $V$ be a finite dimensional representation of $G$ over C. Let $L$ be the descent of the line bundle O(1)^n. We show that the polarised variety $(G\V,L)$ is projectively normal if either $G$ is solvable or $G$ is generated by pseudo reflections. In this proof, we use the combinatorial result of Erd{\o}s-Ginzburg-Ziv. We then show projective normality for solvable groups using toric algebra and deduce the EGZ result as a consequence.