2. (a) Consider the class equation for a finite group G: 18 |G| = |ZG| + G: Cg(91)] 18 Explain briefly (i.e. with one or two sentences each) the meaning of each of the terms on the right hand side of the equation above. [5 marks] (b) Use the class equation to show that the centre of a finite p-group is non trivial. [10 marks] (c) Show that if p is a prime and [G] = p2 then G is abelian. [10 marks]