---
tag: 0Q5G5DJ4P2
kind: concept
name: Derived series
msc: [20F14]
sources:
  - url: https://en.wikipedia.org/wiki/Commutator_subgroup
    locator: Derived series
---

## Summary

The derived series of a group is the sequence of iterated commutator subgroups $G \supseteq G' \supseteq G'' \supseteq \cdots$.
A group is solvable if and only if this series reaches the trivial subgroup.