---
tag: 0ASGSTXSBW
kind: concept
name: Commutator subgroup
aliases: [derived-subgroup]
msc: [20F12]
sources:
  - url: https://en.wikipedia.org/wiki/Commutator_subgroup
    locator: Definition
same_as:
  wikidata: Q522216
  wikipedia: Commutator subgroup
---

## Summary

The commutator subgroup of a group is the subgroup generated by all commutators.
It is the smallest normal subgroup with an abelian quotient.