The finitude of tamely ramified pro-$p$ extensions of number fields with cyclic $p$-class groups

Yoonjin Lee, Donghyeok Lim

Let $p$ be an odd prime and $F$ be a number field whose $p$-class group is cyclic. Let $F_{\{\mathfrak{q}\}}$ be the maximal pro-$p$ extension of $F$ which is unramified outside a…