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.
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.