The composition of two group homomorphisms is a homomorphism

https://arbital.com/p/composition_of_group_homomorphisms_is_homomorphism

by Patrick Stevens Jun 14 2016 updated Jun 14 2016

The collection of group homomorphisms is closed under composition.


Given two group homomorphisms and , the composition is also a homomorphism.

To prove this, note that since is a homomorphism; that is because is a homomorphism.