A group set is a set whose elements are acted on by a group. If the group G acts on the set S, then S is called a G-set. Let G be a group and let S be a G-set. Then for every element s of S and every element g of G, an element g s of S is associated in such a way that e s = s, where e is the identity element of G and such that (g_1 g_2) s = g_1(g_2 s) for every pair of elements g_1, g_2 element s.

G-set