I do not understand Theorem (12.12) at page 81 in Neukirch, Algebraic Number Theory. I can verify each line of the proof, but the following is so clear?
{\bf Problem} Let $o$ be an order in an algebraic number field $K$. Let $f$ be the conductor of $o$, i.e. the biggest ideal of the integral closure $\tilde{o}$ which is contained in $o$. Then, is the number of the units $(o/f)^*$ finite?