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

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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

...

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