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- Let G be a group with center Z(G)=C. Prove that if G/C is cyclic, then G is abelian.Find the normalizer of the subgroup (1),(1,3)(2,4) of the octic group D4.27. a. Show that a cyclic group of order has a cyclic group of order as a homomorphic image. b. Show that a cyclic group of order has a cyclic group of order as a homomorphic image.