Let f: G H be an injective homomorphism of groups. Prove G is abelian if H is abelian.
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- True or False Label each of the following statements as either true or false. 2. Any two abelian groups of the same order are isomorphic.Let G be an abelian group of order 2n, where n is odd. Use Lagranges Theorem to prove that G contains exactly one element of order 2.Suppose ab=ca implies b=c for all elements a,b, and c in a group G. Prove that G is abelian.