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    Characterization of abelian groups

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    a. Show that the function f : G ----> defined by f(x) = x^(-1) is a group homomorphism if and only if G is abelian

    b. Define a new group H to have the same elements as G, but the operation x # y = yx, where yx is defined by the operation in G. Show that the function f : G ----> H defined by f (x) = x ^ (-1) is an isomorphism of G onto H

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    Solution Summary

    The expert examines a characterization of abelian groups. A new group H element is defined.