---
tag: 0Z5905Q73D
kind: concept
name: Alternating group
msc: [20B30]
sources:
  - url: https://en.wikipedia.org/wiki/Alternating_group
    locator: lead section
same_as:
  wikidata: Q438814
  wikipedia: Alternating group
---

## Summary

The alternating group $A_n$ is the group of the even permutations of $n$ symbols.
It is a normal subgroup of index $2$ in $S_n$ for $n \geq 2$.