---
tag: 06QYRTX9KQ
kind: concept
name: P-group
aliases: [p-group]
msc: [20D15]
sources:
  - url: https://en.wikipedia.org/wiki/P-group
    locator: lead section
same_as:
  wikidata: Q286972
  wikipedia: P-group
---

## Summary

For a prime number $p$, a $p$-group is a group in which the order of each element is a power of $p$.
A finite group is a $p$-group if and only if its order is a power of $p$.