Let G be a finite abelian group. Consider the function f:G→G defined by f(x)=x3 (a) Prove f is an homomorphism. (b) If ∣G∣ is not divisible by 3 , prove that f is an isomorphism. (c) If k is the number of elements of G of order 3 , prove that 1+k divides ∣G∣.