Question

let ϕ : g → h be a homomorphism. (a) show that if h is abelian and ϕ is one-to-one, then g is abelian. (b) show that if g is abelian and ϕ is onto, then h is abelian. (c) if ϕ is an isomorphism, show that g is abelian if and only if h is.