Suppose g is a simple group, in the sense that the only normal subgroups of g are {e} and g. show that if b is not the identity element e of g, then either g is abelian or zg(c(b)) = {e}. in other words, no non-trivial element of a non-abelian simple group commutes with every element of a nontrivial conjugacy class. (hint: use part (b) and consider the center z(g) of g.)