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    Automorphism of a group

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    Modern Algebra
    Group Theory (LXI)
    Automorphism of a Group

    Is the mapping given below an automorphism of the group ?
    G group of integers under addition, T:x --> -x

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    Solution Preview

    The solution of the Posting is in the attached file.

    Is the mapping given below an automorphism of the group ?
    group of integers under addition,

    Solution:- Let be a mapping .

    is well defined.

    For , where

    ...

    Solution Summary

    This shows how to determine if a given mapping is an automorphism. The solution is detailed and well presented.

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