In 1955 Chevalley gave a uniform proof the the <a href="https://en.wikipedia.org/wiki/Chevalley%E2%80%93Shephard%E2%80%93Todd_theorem">Chevalley-Shephard-Todd theorem</a> which says that for a finite group $G$ acting on a complex vector space $V$, the following are equivalent: (i) The algebra $S(V)^G$ of invariant polynomial functions on $V$ is a polynomial ring; (ii) $G$ is generated by pseudoreflections. I believe Serre observed that Chevalley's proof of (i) $\Rightarrow$ (ii) goes through verbatim in the case of a field of arbitrary characteristic (although (ii) $\Rightarrow$ (i) may fail).