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 $1959$.
Sources
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 6.5$. Orbits: Example $121$
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: The Sylow Theorems: $\S 56$. First Sylow Theorem
- 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $11$: The Sylow Theorems: Summary for Chapter $11$