# Jordan’s theorem (multiply transitive groups)

Let $G$ be a sharply $n$-transitive permutation group, with $n\geq 4$. Then

1. 1.

$G$ is similar to $S_{n}$ with the standard action or

2. 2.

$G$ is similar to $A_{n+2}$ with the standard action or

3. 3.

$n=4$ and $G$ is similar to $M_{11}$, the Mathieu group of degree $10$ or

4. 4.

$n=5$ and $G$ is similar to $M_{12}$, the Mathieu group of degree $11$.

Title Jordan’s theorem (multiply transitive groups) JordansTheoremmultiplyTransitiveGroups 2013-03-22 13:16:42 2013-03-22 13:16:42 bwebste (988) bwebste (988) 6 bwebste (988) Theorem msc 20B20