---
tag: 0RRWNMYRXC
kind: concept
name: Fixed points of an action
aliases: [fixed-point-set]
msc: [20B05]
sources:
  - url: https://en.wikipedia.org/wiki/Group_action
    locator: Fixed points and stabilizer subgroups
---

## Summary

A fixed point of a group action is a point that each element of the group keeps in place.
The fixed points are exactly the points whose orbit has one element.