Isomorphisms of Galois groups of solvably closed Galois extensions
Isomorphisms of Galois groups of solvably closed Galois extensions
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可解闭伽罗瓦扩张的伽罗瓦群的同构
DOI：
10.2748/tmj/1178229803
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发表时间：
1981
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
这是文[3]中一个定理的推广，也是文[4]中关于有限常数域上代数函数域的一个定理的精确类比。在下文中，Q总是表示有理数的域。\A\表示有限集合A的元素个数。设g是群G中的元素。则C（g）表示包含g的共轭类。设kx和k2是有限次代数数域。然后kt和k2被称为算术等价，如果每个素数在kx和k2中以相同的方式分解[2]。LEMMA 1.设k1，k2和L是有限次代数数域.我们假设L在Q上是正规的。如果k1和k2是算术等价的，则kxL（resp. k^（k L）和k2 L {分别k2 <$L）是算术等价的。
This is a generalization of a theorem in [3], and is the exact analogue of a theorem in [4] for algebraic function fields over finite constant fields. In what follows, Q always denotes the field of the rational numbers. \A\ denotes the number of elements for a finite set A. Let g be an element of a group G. Then C{g) denotes the conjugate class containing g. Let kx and k2 be algebraic number fields of finite degrees. Then kt and k2 are called arithmetically equivalent if every prime number is decomposed in the same manner in kx and k2 [2]. LEMMA 1. Let klf k2 and L be algebraic number fields of finite degrees. We assume L is normal over Q. If k1 and k2 are arithmetically equivalent, kxL (resp. k^ (Ί L) and k2L {resp. k2 Π L) are arithmetically equivalent.