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Let G be a group and define the center (of G) Z(G) = {a ∈ G...

Let G be a group and define the center (of G) Z(G) = {a ∈ G | xa = ax, ∀ x ∈ G}

a. Prove that Z(G) forms a subgroup of G.

b. If G is abelian, show that Z(G) = G.

c. What is the center of S3

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