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Suppose φ : G → G′ is an isomorphism. (a) Prove that φ(Z(G)) = Z(G′). (b)...

Suppose φ : G → G′ is an isomorphism.

(a) Prove that φ(Z(G)) = Z(G′).
(b) Prove that |g| = |φ(g)| for all g ∈ G

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