Jordan’s theorem (multiply transitive groups)
Let $G$ be a sharply $n$transitive^{} permutation group^{}, with $n\ge 4$. Then

1.
$G$ is similar to ${S}_{n}$ with the standard action or

2.
$G$ is similar to ${A}_{n+2}$ with the standard action or

3.
$n=4$ and $G$ is similar to ${M}_{11}$, the Mathieu group^{} of degree $10$ or

4.
$n=5$ and $G$ is similar to ${M}_{12}$, the Mathieu group of degree $11$.
Title  Jordan’s theorem (multiply transitive groups) 

Canonical name  JordansTheoremmultiplyTransitiveGroups 
Date of creation  20130322 13:16:42 
Last modified on  20130322 13:16:42 
Owner  bwebste (988) 
Last modified by  bwebste (988) 
Numerical id  6 
Author  bwebste (988) 
Entry type  Theorem 
Classification  msc 20B20 