I don't have a solid understanding of generators. I understand that you need relatively prime powers to map out all the functions through multiplication. Going by this, I suppose the generators would be 1,3,5,7, & 9, all the odd numbers below 10. For what reason are would these be automorphisms...
Homework Statement
Find all the automorphisms of a cyclic group of order 10.
Homework Equations
ψ(a)ψ(b)=ψ(ab)
For G= { 1, x, x^2,..., x^9}, and some function
ψ(a) = x^(a/10)
The Attempt at a Solution
I know that a homomorphism takes the form
Phi(a)*phi(b) = phi (ab)...