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Aug 28, 2021 at 1:32 comment added Michael Zieve This proof is reminiscent of Dickson's proof. Dickson gave group-theoretic arguments that closely resemble Riemann-Hurwitz, but that don't seem to precisely translate into the language of algebraic geometry.
Aug 22, 2021 at 17:37 history edited LSpice CC BY-SA 4.0
`\DeclareMathOperator`; one case of $|G|$ should be $G$
Aug 22, 2021 at 5:36 comment added abx Very interesting, thanks. A poor man's classification of the subgroups, which is more than sufficient to get the result. Since I cannot accept two answers, I accepted Wojowu's which is closer to what I expected — I hope you don't mind!
Aug 21, 2021 at 19:09 history answered David E Speyer CC BY-SA 4.0