Sylow p-Subgroups of Group of Order 2p/Proof 3

Theorem

Let $p$ be an odd prime.

Let $G$ be a group of order $2 p$.

Then $G$ has exactly one Sylow $p$-subgroup.

This Sylow $p$-subgroup is normal.

Proof

This is a specific instance of Group of Order $p q$ has Normal Sylow $p$-Subgroup, where $q = 2$.

$\blacksquare$