On the structure of the Galois group of the maximal pro-$p$ extension with restricted ramification over the cyclotomic ${\mathbb{Z}}_p$-extension

Tsuyoshi Itoh

Let $k_{\infty }$ be the cyclotomic ${\mathbb{Z}}_p$-extension of an algebraic number field $k$. We denote by $S$ a finite set of prime numbers which does not contain $p$, and $S(k_\inf…