---
tag: 0WCY42EV9V
kind: concept
name: Group action
msc: [20B05]
sources:
  - url: https://en.wikipedia.org/wiki/Group_action
    locator: lead section
same_as:
  wikidata: Q288465
  wikipedia: Group action
---

## Summary

An action of a group $G$ on a set $X$ lets each element of $G$ move the points of $X$. The moves must respect the group operation.
Equivalently, it is a group homomorphism from $G$ to the symmetric group of $X$.