##  [Group Homomorphism](/group-homomorphism) 

  ##  [Group Homomorphism](https://algebra.quantumdictionary.io/group-homomorphism-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A function f: G → H between groups that preserves the group operation: for all a,b in G, f(ab) = f(a)f(b); homomorphisms map identity to identity and inverses to inverses, and their kernels and images are central invariants.