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Let $G$ be a finite group and
$\rho : G \hra \GL(n, \C)$ a complex representation.
Barbara Schmid has shown that the algebra of invariant
polynomial functions $\C[V]^G$ on the vector space $V = \C^n$ is generated by
homogeneous polynomials of degree at most $\beta$\/, where $\beta$ is the
largest degree of a generator in a minimal generating set for
$\C[\reg_\C(G)]^G$\/, and $\reg_\C(G)$ is the complex regular representation
of $G$\/. In this note we give a new proof of this result, and at the same
time extend it to fields $\F$ whose characteristic $p$ is larger than
$|G|$\/, the order of the group $G$\/.