---
tag: 0Q7MMQHC1P
kind: concept
name: Nilpotent group
msc: [20F18]
sources:
  - url: https://en.wikipedia.org/wiki/Nilpotent_group
    locator: Definition
same_as:
  wikidata: Q1755242
  wikipedia: Nilpotent group
---

## Summary

A nilpotent group is a group that has a central series of finite length.
Equivalently, its lower central series reaches the trivial subgroup, or its upper central series reaches the whole group.