Question

Identify the automorphism
group of Z64?

Answer 1

@TheSmartOne @robtobey @ganeshie8 Help!

Answer 2

I was looking up how to do this and this hint seems very useful: If \(\phi()\) is an automorphism, then \(\forall x \in Z_{64}\), the order of \(x\) must be the same as the order of \(\phi(x)\)... that will help you narrow stuff down. And of course, the automorphism group can be thought of, as a subset of a symmetric group.

Answer 3

\[Aut(Z_n)\approx U(n)\] for \(n\in\mathbb{Z}^{+}\)