Where can I find Wielandt's original proof of Sylow's Theorem?

Question

I have seen several proofs of Sylow's Theorem based on Wielandt's method. Everyone gives credit to Wielandt's proof of Sylow's theorem, but ironically everyone puts their own spin on it.

Where can I find the original Wielandt's proof of Sylow's theorem?

Answer 1

At the end of the Wikipedia page for that, it gave this citation: Wielandt, Helmut Ein Beweis für die Existenz der Sylowgruppen. (German) Arch. Math. (Basel) 10 1959 401–402.

And then I found this scanned page that mentions that paper in a condensed way.

My German is rusty, but I can kind of see that it says something like

The following very simple proof for the existence of Sylow groups of a group $\def\G{\frak G}\G$ is given: Let $p^n$ be a divisor of the order $g$ of $\G$, with $p$ a prime number. We consider the $\binom g{p^n}$ subsets of cardinality $p^n$ of $\G$. On them $\G$ realises by right-multiplication a permutation representation of $\G$. As $p^{n+1}$ is not a divisor of $\binom g{p^n}$, there is some orbit [area of transitivity] of length not divisible by $p^{n+1}$. If $\frak K$ is a set in this orbit, then the stabiliser subgroup of $\frak K$ [the subgroup $\frak H$ that fixes $\frak K$] has the desired order $p^k$.