On separating a fixed point from zero by invariants

摘要

Assume a fixed point vV(G) can be separated from zero by a homogeneous invariant f?V(G) of degree p(r)d, where p>0 is the characteristic of the ground field ? 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.