Let G be a Group. The center of, denoted by Z(G), is defined tobe the set of all elements of G that with every element of G.Symbolically, we have
Z(G) = {x in G | ax=xa for all a in G}.
(a) Prove that Z(G) is a subgroup of G.
(b) Prove that Z(G) is an Abelian group.
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