---
tag: 0WE2NHZJ7B
kind: concept
name: Order of an element
aliases: [period-of-an-element]
msc: [20A05]
sources:
  - url: https://en.wikipedia.org/wiki/Order_(group_theory)
    locator: lead section
---

## Summary

The order of an element of a group is the smallest positive integer $n$ such that the $n$th power of the element is the identity.
When no such $n$ exists, the element has infinite order.