Recall that the center of a group G is Z(G)={x∈G:xg=gx,∀g∈G}. That is, the set of all elements which commute with every element of G. Use the following definition of a subgroup H being a normal subgroup to show that Z(G)is a normal subgroup of G:A subgroup H of G is a normal subgroup of G if for all g∈G we have g^(-1) Hg=H.