Definition:Sylow p-Subgroup/Definition 3
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Let $p$ be prime.
Let $n$ be the largest integer such that:
- $p^n \divides \order G$
where $\divides$ denotes divisibility.
A Sylow $p$-subgroup is a $p$-subgroup of $G$ which has $p^n$ elements.
Source of Name
This entry was named for Peter Ludwig Mejdell Sylow.
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 6.5$. Orbits: Example $121$
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Exercise $25.18$
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: The Sylow Theorems: $\S 56$. First Sylow Theorem