---
tag: 0AYMP41THN
kind: concept
name: Stabiliser
aliases: [stabilizer, isotropy-group]
msc: [20B05]
sources:
  - url: https://en.wikipedia.org/wiki/Group_action
    locator: Fixed points and stabilizer subgroups
---

## Summary

The stabiliser of a point $x$ under a group action is the set of the group elements that do not move $x$.
It is a subgroup of the group.