 That is, assuming (without a real loss of generality) that formula_1 acts on the left of formula_2, for each pair of pairs formula_6 with formula_7 and formula_8, there exists a formula_9 such that formula_10.Equivalently, formula_11 and formula_12, since the induced action on the distinct set of pairs is formula_13.Every 2-transitive group is a primitive group, but not conversely.