# Automorphism of a group

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

https://brainmass.com/math/linear-transformation/automorphism-group-65681

#### 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.