Example 1

Let G be a group, and let $\mathscr{G}$ be the groupoid associated with G (II, p. 163, Example 1). If X is a set, an operation (on the right) of the groupoid $\mathscr{G}$ on X is nothing other than an operation (on the right) of the group G on X. Moreover, the orbits of the operation of $\mathscr{G}$ coincide with those of the group G.