# Finite normal subgroup

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)



## [Finite normal subgroup](https://ocme.evemisslab.com/en/atlas/atlas-finite-normal-subgroup/)

A subgroup H of a finite group G is normal when gHg^(-1)=H for every g, equivalently when each left coset equals the corresponding right coset.

atlas-finite-normal-subgroup · canonical_mko

[Finite normal subgroup](https://ocme.evemisslab.com/en/mko/mko-finite-normal-subgroup/)

## Prerequisite nodes


- [Finite group](https://ocme.evemisslab.com/en/atlas/atlas-finite-group/)
- [Subgroups and group homomorphisms](https://ocme.evemisslab.com/en/atlas/atlas-subgroup-homomorphism/)
- [Quantifiers and explicit domains](https://ocme.evemisslab.com/en/atlas/atlas-quantifier/)