  Assume a fixed point v in a G-module V can be separated from zero by a
homogeneous invariant of degree dp^r where p>0 is the characteristic of the
ground field k and p, d are coprime. We show that then v can also be separated
from zero by an invariant of degree p^r , which we obtain explicitly from f. It
follows that the minimal degree of a homogeneous invariant separating v from
zero is a p-power.
