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    Automorphism proof

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    Prove the following theorem:

    is an automorphism of under componentwise addition.

    Additional Notes on the Task:
    Be careful not to confuse the homomorphism's action as a function with the group operation's action as componentwise addition.
    is componentwise addition where and in . How would you show the function is a morphism using X, Y, and X + Y ?

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    Solution Summary

    This provides an example of an automorphism proof.