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In 1955 Chevalley gave a uniform proof the the Chevalley-Shephard-Todd theorem 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).

EDIT: Whoops, according to comments at a previous MO question (Chevalley–Shephard–Todd theorem), I might be conflating two things here- the issue of the characteristic of the field, and the issue of reflections versus pseudoreflections. I think what Serre actually observed regarding Chevalley's proof is that the implication (ii) $\Rightarrow$ (i) is true for pseuoreflections, whereas Chevalley had only stated it for reflections.

A scan of the relevant paper "Groupes finis d’automorphismes d’anneaux locaux réguliers" of Serre (in French) is here: https://www.math.purdue.edu/~wilker/misc/serre-enjf.pdf.

In his 1955 paper "Invariant of finite groups generated by reflections" Chevalley gave a uniform proof the the Chevalley-Shephard-Todd theorem 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.

Actually Chevalley only proved (ii) $\Rightarrow$ (i); the other implication already had a uniform proof in Shephard and Todd's original work, and anyways is not hard once you know (ii) $\Rightarrow$ (i).

However, Chevalley only stated his result for reflections (i.e., pseudoreflections of order 2) because he was mostly only interested in Weyl groups, and in fact as far as I can tell he was not aware of the work of Shephard and Todd. 

Serre observed, in his 1967 paper "Groupes finis d’automorphismes d’anneaux locaux réguliers", that Chevalley's proof goes through verbatim in the case of pseudoreflections, because he only ever uses the fact that the reflections fix a hyperplane, and not that they have order 2.

(In that paper Serre also studies pseudoreflection groups over fields of positive characertistic, where (i) and (ii) are no longer necessarily equivalent.)

For more discussion of the history of the Chevalley-Shephard-Todd theorem, see this previous MO question: Chevalley–Shephard–Todd theorem.

In 1955 Chevalley gave a uniform proof the the Chevalley-Shephard-Todd theorem 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).

EDIT: Whoops, according to comments at a previous MO question (Chevalley–Shephard–Todd theorem), I might be conflating two things here- the issue of the characteristic of the field, and the issue of reflections versus pseudoreflections. I think what Serre actually observed regarding Chevalley's proof is that the implication (i) $\Rightarrow$ (ii) is true for pseuoreflections, whereas Chevalley had only stated it for reflections.

A scan of the relevant paper "Groupes finis d’automorphismes d’anneaux locaux réguliers" of Serre (in French) is here: https://www.math.purdue.edu/~wilker/misc/serre-enjf.pdf.

In 1955 Chevalley gave a uniform proof the the Chevalley-Shephard-Todd theorem 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).

EDIT: Whoops, according to comments at a previous MO question (Chevalley–Shephard–Todd theorem), I might be conflating two things here- the issue of the characteristic of the field, and the issue of reflections versus pseudoreflections. I think what Serre actually observed regarding Chevalley's proof is that the implication (ii) $\Rightarrow$ (i) is true for pseuoreflections, whereas Chevalley had only stated it for reflections.

A scan of the relevant paper "Groupes finis d’automorphismes d’anneaux locaux réguliers" of Serre (in French) is here: https://www.math.purdue.edu/~wilker/misc/serre-enjf.pdf.

In 1955 Chevalley gave a uniform proof the the Chevalley-Shephard-Todd theorem 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).

EDIT: Whoops, according to comments at a previous MO question (Chevalley–Shephard–Todd theorem), I might be conflating two things here- the issue of the characteristic of the field, and the issue of reflections versus pseudoreflections. I think what Serre actually observed regarding Chevalley's proof is that the implication (i) $\Rightarrow$ (ii) is true for pseuoreflections, whereas Chevalley had only stated it for reflections.

In 1955 Chevalley gave a uniform proof the the Chevalley-Shephard-Todd theorem 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).

EDIT: Whoops, according to comments at a previous MO question (Chevalley–Shephard–Todd theorem), I might be conflating two things here- the issue of the characteristic of the field, and the issue of reflections versus pseudoreflections. I think what Serre actually observed regarding Chevalley's proof is that the implication (i) $\Rightarrow$ (ii) is true for pseuoreflections, whereas Chevalley had only stated it for reflections.

A scan of the relevant paper "Groupes finis d’automorphismes d’anneaux locaux réguliers" of Serre (in French) is here: https://www.math.purdue.edu/~wilker/misc/serre-enjf.pdf.