Let G be a finite group. Suppose that Phi: G -> S.4 is a homomorphism and phi is onto. Prove that G is not abelian. Prove that G contains an element of order 4. Let H = { a G \ phi(a) A4 }. Prove that if is a subgroup of G. Determine whether the subgroup H defined in part c) is a normal subgroup of G.
