# Cauchy theorem for finite groups

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

[Catalogue presentation and source-binding data](https://ocme.evemisslab.com/data/i18n/catalogue.en.json)



## [Cauchy theorem for finite groups](https://ocme.evemisslab.com/en/atlas/atlas-cauchy-theorem-finite-groups/)

If a prime p divides the order of a finite group G, G contains an element of exact order p.

atlas-cauchy-theorem-finite-groups · canonical_mko

[Cauchy theorem for finite groups](https://ocme.evemisslab.com/en/mko/mko-cauchy-theorem-finite-groups/)

## Prerequisite nodes


- [Lagrange theorem for finite groups](https://ocme.evemisslab.com/en/atlas/atlas-lagrange-theorem-finite-groups/)
- [Prime natural number](https://ocme.evemisslab.com/en/atlas/atlas-prime-number/)
- [Finite group](https://ocme.evemisslab.com/en/atlas/atlas-finite-group/)
- [Finite group action](https://ocme.evemisslab.com/en/atlas/atlas-finite-group-action/)