---
type: "concept"
title: "Permutation"
slug: "permutation"
language: "en"
translationGroupId: "cmrc5gjq80009s701p9o7sq34"
domain: "Algebra"
status: "usable"
aliases: []
lastEditedBy: "ancient-tree"
---

A permutation of a set $X$ is a [[Bijective map|bijection]] $\sigma:X \rightarrow X$.

##### Remarks
- The set of permutations of $X$ forms a [[Group|group]] under [[Composition of maps|composition]], denoted $\mathfrak{S}_X$ or $S(X)$.