Definition:Kernel of Group Action

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:
 * $\left\{{g \in G: \forall x \in X: g \cdot x = x}\right\}$

The kernel can be denoted $G_0$

Also see

 * Definition:Faithful Group Action