Question: what are the properties of group homomorphism?
Answer: Properties of Homomorphisms Composition: The composition of homomorphisms is a homomorphism. That is, if f ⁣ : A → B f \colon A \to B f:A→B and g ⁣ : B → C g \colon B \to C g:B→C are homomorphisms, then g ∘ f ⁣ : A → C g \circ f \colon A \to C g∘f:A→C is a homomorphism as well.