Definition:Effective Transformation Group

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

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

$$\forall x \in X: g \wedge x = x \Longrightarrow g = e$$

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