---
tag: 0YGN3VAA0D
kind: concept
name: Normaliser
aliases: [normalizer]
msc: [20A05]
sources:
  - url: https://en.wikipedia.org/wiki/Centralizer_and_normalizer
    locator: Definitions
---

## Summary

The normaliser of a subset $S$ of a group $G$ is the set of elements $g$ with $gSg^{-1} = S$.
It is the largest subgroup in which a given subgroup is normal.