GALOIS GROUPS OF UNRAMIFIED SOLVABLE EXTENSIONS
GALOIS GROUPS OF UNRAMIFIED SOLVABLE EXTENSIONS
复制标题
非拉曼可解扩展的伽罗瓦群
DOI：
10.2748/tmj/1178229257
复制
发表时间：
1982
影响因子：
0.5
通讯作者：
Kôji Uchida
中科院分区：
文献类型：
--
作者：
Kôji Uchida
在本文中，Q，Z和e;n表示有理数，有理数整数和正整数n的本原n次单位根。设F是有限次代数数域.我们不知道任何一般的方法来确定结构的伽罗瓦群的最大unramified（可解）扩张的F。我们所说的“非分歧”是指每个有限或无限素数都是非分歧的。设Fn = F（e;n）且F==UnFn。A.布鲁默最近证明，
Throughout this paper, Q, Z and e;n denote the rational numbers, the rational integers and a primitive n-th root of unity for a positive integer n. Let F be an algebraic number field of finite degree. We do not know any general method of determining the structure of the Galois group of the maximal unramified (solvable) extension of F. We mean by "unramified" that every finite or infinite prime is unramified. Let Fn = F(e;n) and let F==UnFn. A. Brumer recently proved that