A group set is a set whose elements are acted on by a group. If the group acts on the set , then is called a G-set.

Let be a group and let be a G-set. Then for every element of and every element of , an element of is associated in such a way that , where is the identity element of and such that for every pair of elements .

The multiplication of elements of by elements of described above is called a left -action, since the elements of are multiplied on the left. For this reason, is sometimes called a left -set. Right -sets are defined analogously to left -sets except that multiplication by elements of is now performed to the right of elements of .