Definition:Faithful 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.

$\phi$ is faithful or effective :
 * $\forall g \in G : ( \forall x \in X: g * x = x \implies g = e)$

That is, $G$ is an effective transformation group if the Identity Group Action‎ $G_0$ equals $\left\{{e}\right\}$.