---
tag: 0ZDW0H0VX4
kind: concept
name: Exponent of a group
msc: [20F50]
sources:
  - url: https://en.wikipedia.org/wiki/Torsion_group
    locator: lead section
---

## Summary

The exponent of a group is the least positive integer $n$ with $g^n = e$ for each element $g$, when such an integer exists.
It is the least common multiple of the orders of the elements.