Isomorphism between two groups mapping the same elements I need to show that there is an isomorphic function $f:\Bbb Z_6 \to U(14)$ that $f(5)=5$
I can show that $U(14)$ is isomorphic to $\Bbb Z_6$ by showing that $U(14)$ is cyclic of order 6, but I do not know whether this would imply that $\Bbb Z_6$ is isomorphic to $U(14)$. Can I make this inference? Also, how do I now show that $f(5)=5$?
Help would be greatly appreciated.
Thanks in advance!

Note that if there exists an isomorphism f: G ----> G', f^-1 is an isomorphism from G' to G. (If f is a bijection, then it inverse is as well, and t is easy to check that the condition for isomorphisms hold for inv(f). 
