Definition:Kernel of Group Action/Definition 1

Definition
Let $G$ be a group with identity $e$.

Let $X$ be a set.

Let $\phi : G\times X\to X$ be a group action.

The kernel of the group action is the set:
 * $G_0 = \left\{{g \in G: \forall x \in X: g \cdot x = x}\right\}$