Ferrero-Washington theorem ($\mu (Y)=0$)

For a finite abelian extension of $\mathbb{Q}$, the unramified Iwasawa module of its cyclotomic Zp-extension has $\mu =0$. This removes $p$-power elementary factors from its characteristic ideal. The theorem does not assert $\mu =0$ for arbitrary noncyclotomic Zp-extensions.