let G be a finite group

if sigma is automorphism from G to G such that

given that is the identity automorphism

prove that G is abelian ( hint prove that every element of G can be written as apply sigma to such expression

as you can see I end up with what I am asking about, did I made something wrong?

I work in it in another way

since sigma^2 is the identity

let

so if x image is x* then x* image is x