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% squeeze.txt : summary of contents of squeeze.ps
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Let $\rho : G \hookrightarrow \GL(n,\ \F)$ be a faithful representation of the finite group
$G$ over the field $\F$\/. In 1916 E. Noether proved that
for $\F$ of characteristic zero the ring of
invariants $\F[V]^G$ is generated as an algebra by the invariant polynomials of
degree at most $|G|$\/. This result has been generalized to the case
where the characteristic of $\F$ is
greater than $|G|$\/, or when the characteristic of $\F$ is prime to the
order of $G$ and the group $G$ is solvable.
In this note we prove that if Noether's bound fails in the nonmodular case,
then it fails for a finite nonabelian simple group.
We then show how yet another reworking of Noether's argument leads to a
proof that Noether's bound holds in the nonmodular case for the alternating groups.