Transitivity of Groups

Multiply Transitive Groups

-Transitivity

Suppose is a set and is a group acting on . The action of on is called -transitive if the induced action on is transitive. That is, for any two -tuples and of distinct elements of , there exists an element such that for all . If, in addition, such is unique, then the action is called sharply -transitive.
A group is called -transitive if it admits an -transitive action on some set .

Mathieu Group