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    Show that the group G is abelian if (ab)^2=a^2b^2

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    Modern Algebra
    Group Theory (VIII)

    If G is a group such that (ab)^2=a^2b^2 for all a,b belongs to G, show that G must be abelian.

    Or, Show that the group G is abelian iff (ab)^2=a^2b^2.

    The fully formatted problem is in the attached file.

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    Solution Summary

    This shows how to complete a proof regarding an Abelian group. The solution is detailed and well presented.