[[Group theory MOC]]
# Permutation group

A **permutation group** is a _concept with an attitude_ essentially corresponding to a faithful [[group action]].
Specifically, a permutation group $G$ is a [[subgroup]] of the [[symmetric group]] $\Omega!$ for some **ground set** $\Omega$. #m/def/group 
Since by [[Cayley's theorem]] every group can be made into a permutation group, the point is that $G$ is equipped with a _canonical_ action on $\Omega$.

## Terminology

- [[Multiply transitive permutation group]]

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#state/tidy | #lang/en | #SemBr