I have to show that U(140) is isomorphic to U(144). I understand that $U(140)=U(2^2)+U(5)+U(7)$ and $U(144)=U(2^4)+U(3^2)$. How can I use this fact and the fact to show that its isomorphic?
I have completed this step, but now I am stuck on the part below.
Also, Show that U(pq) is never cyclic for p and q are distinct odd primes. Any tips?