---
tag: 0GETX79CJN
kind: concept
name: Normal core
aliases: [core-of-a-subgroup]
msc: [20D25]
sources:
  - url: https://en.wikipedia.org/wiki/Core_(group_theory)
    locator: The normal core
same_as:
  wikidata: Q3010804
  wikipedia: Core (group theory)
---

## Summary

The normal core of a subgroup $H$ of a group $G$ is the largest normal subgroup of $G$ that is contained in $H$.
It is the intersection of all conjugates of $H$.