# multiply transitive

Let $G$ be a group, $X$ a set on which it acts. Let $X^{(n)}$ be the set of order $n$-tuples of distinct elements of $X$. This is a $G$-set by the diagonal action:

 $g\cdot(x_{1},\ldots,x_{n})=(g\cdot x_{1},\ldots,g\cdot x_{n})$

The action of $G$ on $X$ is said to be $n$-transitive if it acts transitively on $X^{(n)}$.

For example, the standard action of $S^{n}$, the symmetric group, is $n$-transitive, and the standard action of $A_{n}$, the alternating group, is $(n-2)$-transitive.

Title multiply transitive MultiplyTransitive 2013-03-22 13:16:37 2013-03-22 13:16:37 bwebste (988) bwebste (988) 5 bwebste (988) Definition msc 20B20 $n$-transitive