# First isomorphism 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)



## [First isomorphism theorem for finite groups](https://ocme.evemisslab.com/en/atlas/atlas-first-isomorphism-theorem-finite-groups/)

A finite group homomorphism induces an isomorphism from its kernel quotient to its image, not automatically to the entire codomain.

atlas-first-isomorphism-theorem-finite-groups · canonical_mko

[First isomorphism theorem for finite groups](https://ocme.evemisslab.com/en/mko/mko-first-isomorphism-theorem-finite-groups/)

## Prerequisite nodes


- [Kernel of a finite group homomorphism](https://ocme.evemisslab.com/en/atlas/atlas-finite-group-homomorphism-kernel/)
- [Finite quotient group](https://ocme.evemisslab.com/en/atlas/atlas-finite-quotient-group/)
- [Subgroups and group homomorphisms](https://ocme.evemisslab.com/en/atlas/atlas-subgroup-homomorphism/)
- [Bijectivity and unique preimages](https://ocme.evemisslab.com/en/atlas/atlas-bijective/)