Multiply transitive group action
SET
Doubly transitive; Two transitive group; Doubly transitive group; Doubly transitive permutation group; 2-transitive permutation group; Doubly-transitive permutation group; Doubly transitive permutation representation; 2-transitive; 2-transitive group
A group G acts 2-transitively on a set S if it acts transitively on the set of distinct ordered pairs \{ (x,y) \in S \times S : x \neq y \}. That is, assuming (without a real loss of generality) that G acts on the left of S, for each pair of pairs (x,y),(w,z)\in S\times S with x \neq y and w\neq z, there exists a g\in G such that g(x,y) = (w,z).