# Definition(s) > [!NOTE] Definition 1 () > Let $\phi$ be an [[Group action|action]] of the finite group $G$ on a set $X$. Let $x\in X$, then the stabilizer of $x$ is given by $\text{Stab}_{G}(x)= \{ g\in G: \phi(g,x)=x \}.$ > [!Example] Example > Contents # Properties(s) Note that [[Stabilizer is Subgroup]]. # Application(s) **More examples**: # Bibliography