Sylow Theorems/Historical Note/First Sylow Theorem

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Historical Note on First Sylow Theorem

Sylow's original work in $1872$ demonstrated the existence of what is now known as a Sylow $p$-subgroup.

The corollary, that there exists a subgroup of order $p^n$ for all $p^n \divides \order G$, was deduced later, but is frequently itself referred to as the First Sylow Theorem.

The proof using the Orbit-Stabilizer Theorem is based on one published by Helmut Wielandt in $1959$.