NUMBER FIELDS WITH CLASS NUMBER CONGRUENT TO 4 MOD 8 AND HILBERTS THEOREM 94
NUMBER FIELDS WITH CLASS NUMBER CONGRUENT TO 4 MOD 8 AND HILBERTS THEOREM 94
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DOI：
10.1016/0022-314x(76)90004-4
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发表时间：
1976-01-01
影响因子：
0.7
通讯作者：
KISILEVSKY, H
中科院分区：
文献类型：
--
作者：
KISILEVSKY, H
设k为一个数域，其理想类群的Sylow 2-子群k与4 -群同构。那么要么希尔伯特类域对k的类数是奇数，要么存在唯一的k的8次非贝尔无分支扩展L。伽罗瓦群g （L k）则是8阶的二面体或四元数群，它们的出现用希尔伯特定理94来表示。在k= Q(−m) 1 2的情况下，m是一个正的无平方整数，我们用整数m的算术性质得到了这个表征。
Let k be a number field with S k, the Sylow 2-subgroup of its ideal class group, isomorphic to the four-group. Then either the class number of the Hilbert class field to k is odd, or there is a unique nonabelian unramified extension L of k of degree 8. The galois group g (L k) is then the dihedral or quaternion group of order 8, and the occurrence of each is characterized in terms of Hilbert's theorem 94. In the case k= Q (− m) 1 2, m a positive square-free integer, we obtain this characterization in terms of arithmetic properties of the integer m.