For an integer n ≥ 1, the action is n -transitive if X has at least n elements, and for any pair of n -tuples (x 1,..., x n), (y 1,..., y n) ∈ X with pairwise distinct entries (that is x i ≠ x j, y i ≠ y j when i ≠ j) there exists a g ∈ G such that g ⋅ x i = y i for i = 1,..., n. In other words the action on the subset of X of tuples without repeated entries is transitive. For n = 2, 3 this is often called double, respectively triple, transitivity. The class of 2-transitive groups (that is, subgroups of a finite symmetric group whose action is 2-transitive) and more generally multiply transitive groups is well-studied in finite group theory.