if G is the abelian group of integers in the mapping T:G to G given by T(x) = x then prove that as an automorphism
Let be the abelian group of integers. Let us show that the mapping given by is an automorphism.
Since we conclude that is a homomorphism.
Since for we get that we conclude that is one-to-one.
Taking into account that for any we have that we conclude that is surjective.
Therefore, is a bijection, and hence is an automorphism.
Comments