Permutation group

Multiply transitive permutation group

A permutation group $𝐺 \subseteq Ω!$ is $𝑘$ -transitive iff it acts on ordered tuples in $Ω P 𝑘$ transitively. #m/def/group

Classification

For $𝑘 \geq 6$ , the only $𝑘$ -transitive groups are $S 𝑛$ with $𝑛 \geq 𝑘$ and $A l t 𝑛$ with $𝑛 \geq 𝑘 + 2$ ;
The only 5-transitive groups that aren't 6-transitive are $M 24$ , Mathieu group M12, $S 5$ , and $A l t 7$ .

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