# Subgroups and group homomorphisms

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)



## [Subgroups and group homomorphisms](https://ocme.evemisslab.com/en/atlas/atlas-subgroup-homomorphism/)

A subgroup is a group under the inherited operation; a group homomorphism preserves multiplication, and its kernel and image follow from the complete map table.

atlas-subgroup-homomorphism · canonical_mko

[Subgroups and group homomorphisms](https://ocme.evemisslab.com/en/mko/mko-subgroup-homomorphism/)

## Prerequisite nodes


- [Finite group](https://ocme.evemisslab.com/en/atlas/atlas-finite-group/)
- [Subset](https://ocme.evemisslab.com/en/atlas/atlas-subset/)
- [Function mapping](https://ocme.evemisslab.com/en/atlas/atlas-function-mapping/)