  Let G < SL(V) be a finite group, V is finite dimensional over a field F,
p=char F and S(V) is the symmetric algebra of V. We determine when the subring
of G-invariants S(V)^G is a polynomial ring. As a consequence, we classify, if
F is algebraically closed, all S(V)^G which are isolated singularities. We show
that the completion of S(V)^G, at its unique graded maximal ideal, is
isomorphic to the completion of S(W)^H, where (H,W) is a reduction mod p of a
member of the Zassenhaus-Vincent-Wolf list of complex isolated quotient
singularities.
