---
type: "concept"
title: "Group homomorphism"
slug: "group-homomorphism"
language: "en"
translationGroupId: "cmraf76610001o801cikip16y"
domain: "Algebra"
status: "stub"
aliases: []
lastEditedBy: "ancient-tree"
---

Let $(G,*)$ and $(H,\cdot)$ be two [[Group|groups]]. A map $f:G \rightarrow H$ is a group homomorphism if for all $a,b\in G$ :
$$f(a*b)=f(a)\cdot f(b)$$