---
tag: 0K98R7A4VC
kind: concept
name: Lower central series
msc: [20F14]
sources:
  - url: https://en.wikipedia.org/wiki/Central_series
    locator: Lower central series
---

## Summary

The lower central series of a group $G$ is the sequence $G = \gamma_1(G) \supseteq \gamma_2(G) \supseteq \cdots$ with $\gamma_{i+1}(G) = [\gamma_i(G), G]$.
The group is nilpotent if and only if this series reaches the trivial subgroup.