Definition:Effective Transformation Group

Definition
Let $G$ be a group whose identity is $e$.

The transformation group $G$ acts effectively on a set $X$ iff:


 * $\forall x \in X: g * x = x \implies g = e$

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