Faithful action

It is said that a group action is effective or faithful if for every two distinct $g,h\in G$ there exists $x\in X$ such that $x\cdot g\ne x\cdot h$, or equivalently, the only element that do not move any point is the identity. It is clear that freeness implies faithfulness. A faithful action tells us that the group can be injected into the bijections group of $X$.