If G is Isomorphic to H then G is Cyclic iff H is Cyclic Proof

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If G is Isomorphic to H then G is Abelian iff H is Abelian Proof If G is Isomorphic to H then G is Abelian iff H is Abelian Proof
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let f be homomorphism and if H is cyclic then f(H) is cyclic let f be homomorphism and if H is cyclic then f(H) is cyclic