Definition:Stabilizer

Theorem
Let $$G$$ be a group which acts on a set $$X$$.

For each $$x \in X$$, the stabilizer of $$x$$ by $$G$$ is defined as:


 * $$\operatorname{Stab} \left({x}\right) \ \stackrel {\mathbf {def}} {=\!=} \ \left\{{g \in G: g * x = x}\right\}$$

Comment
Some authors use $$G_x$$ for the stabilizer of $$x$$ by $$G$$.

The English spelling for it is stabiliser.