Some rings of invariants that are Cohen-Macaulay

Let rho: G hooked right arrow GL(n, F) be a representation of the finite group G over the field F. If the order \G\ of G is relatively prime to the characteristic of F or n = 1 or 2, then it is known that the ring of invariants F[V](G) is Cohen-Macaulay. There are examples to show that F[V](G) need not be Cohen-Macaulay when Iq is divisible by the characteristic off. In all such examples dim(F)(V) is at least 4. In this note we fill the gap between these results and show that rings of invariants in three variables are always Cohen-Macaulay.