Definition:Sylow p-Subgroup/Definition 1

Definition

Let $p$ be prime.

Let $G$ be a finite group whose order is denoted by $\order G$.

Let $\order G = k p^n$ where $p \nmid k$.

A Sylow $p$-subgroup is a $p$-subgroup of $G$ which has $p^n$ elements.

Also see

• Equivalence of Definitions of Sylow $p$-Subgroup

Source of Name

This entry was named for Peter Ludwig Mejdell Sylow.

Sources

• 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $11$: The Sylow Theorems: Definition $11.1$