# Kernel of a finite group homomorphism

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)



## [Kernel of a finite group homomorphism](https://ocme.evemisslab.com/en/atlas/atlas-finite-group-homomorphism-kernel/)

For a finite group homomorphism f:G→Q, the full preimage of the target identity is a normal subgroup of G, and nonempty fibers are its cosets.

atlas-finite-group-homomorphism-kernel · canonical_mko

[Kernel of a finite group homomorphism](https://ocme.evemisslab.com/en/mko/mko-finite-group-homomorphism-kernel/)

## Prerequisite nodes


- [Subgroups and group homomorphisms](https://ocme.evemisslab.com/en/atlas/atlas-subgroup-homomorphism/)
- [Finite normal subgroup](https://ocme.evemisslab.com/en/atlas/atlas-finite-normal-subgroup/)
- [Function mapping](https://ocme.evemisslab.com/en/atlas/atlas-function-mapping/)