Group action

Operation of the elements of a group as transformations or automorphisms (mathematics)

Thus, for establishing general properties of group actions, it suffices to consider only left actions. However, there are cases where this is not possible. For example, the multiplication of a group induces both a left action and a right action on the group itself—multiplication on the left and on the right, respectively.

This result is especially useful since it can be employed for counting arguments (typically in situations where X is finite as well).

A result closely related to the orbit-stabilizer theorem is Burnside's lemma: