---
tag: 0YMYMNQ0QZ
kind: concept
name: Simple group
msc: ["20E32"]
sources:
  - url: https://en.wikipedia.org/wiki/Simple_group
    locator: lead section
same_as:
  wikidata: Q571124
  wikipedia: Simple group
---

## Summary

A simple group is a nontrivial group whose only normal subgroups are the trivial subgroup and the group itself.
The finite simple groups are the building blocks of all finite groups.