论文标题
在希尔伯特（Hilbert
On the Hilbert $2$-class field towers of some cyclotomic $\mathbb{Z}_2$-extensions
论文作者
论文摘要
在本文中，我们研究了$ 2 $级的野外塔的长度以及Galois组的结构$ \ MATHRM {gal}（\ Mathcal {l}（l}（k_n）/k_n）$的最大不符合$ 2 $ 2 $ exters $ k_n $ k_n $ gyclotomic $ $ \ mathbbbbbbbbbbbbbb ighotemal $ 2 $ ext的$ 2 $的长度字段。也研究了投降问题。
In this paper, we study the length of the $2$-class field towers and the structure of the Galois groups $\mathrm{Gal}(\mathcal{L}(K_n)/K_n)$ of the maximal unramified $2$-extensions of the layers $K_n$ of the cyclotomic $\mathbb{Z}_2$-extension of some special Dirichlet fields. The capitulation problem is investigated too.
