I have the following question:
Let $G$ be a group. And $A,B\leq G$ two cyclic subgroups with $|A|=|B|=n$. When does an Automorphism $\alpha\in\mathrm{Aut}(G)$ exists such that $\alpha(A)=B$?
If $n=p$ is prime, does this changes the situation?
Thanks for help.