# Sylow Theorems/Historical Note/First Sylow Theorem

Jump to navigation
Jump to search

## 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 $11$