---
tag: 0PXW0BN7DW
kind: concept
name: Commutator of two elements
msc: [20F12]
sources:
  - url: https://en.wikipedia.org/wiki/Commutator
    locator: Group theory
same_as:
  wikidata: Q2989763
  wikipedia: Commutator
---

## Summary

The commutator of two elements $g$ and $h$ of a group is $[g, h] = g^{-1} h^{-1} g h$.
It is the identity exactly when $g$ and $h$ commute.