---
tag: 0SQTMQTSRZ
kind: concept
name: Even and odd permutations
msc: [20B30]
sources:
  - url: https://en.wikipedia.org/wiki/Parity_of_a_permutation
    locator: lead section
same_as:
  wikidata: Q1064405
  wikipedia: Parity of a permutation
---

## Summary

A permutation of a finite set is even when it is a product of an even number of transpositions, and odd otherwise.
The even permutations form the alternating group.