# Statement(s) > [!NOTE] Statement 1 (Stabilizer is subgroup) > Let $G$ be a group [[Group action|acting]] on set $X$. For all $x\in X$, the [[Stabilizer under Group Action|stabilizer]] of $x$ is a [[Subgroup|subgroup]] of $G$. > # Proof(s) ###### Proof of statement 1: $\blacksquare$ # Application(s) **Consequences**: **Examples**: # Reference(s)