Apt for questions related to stabilizer. Stabilizer of an element $a$ (in a set $M$) is also called the isotropy group of $a$ or the isotropy subgroup of $a$ or the stationary subgroup of $a$.
Let $G$ be a permutation group on a set $\Omega$ and $x$ be an element of $\Omega$. Then $$G_x=\{g \in G:g(x)=x\}$$ is called the stabilizer of $x$ and consists of all the permutations of $G$ that produce group fixed points in $x$, i.e., that send $x$ to itself.
