On exceptional pq-groups  

作　　者：BROWKIN Jerzy XU KeJian 

机构地区：[1]Institute of Mathematics,Polish Academy of Sciences,Warsaw PL-00-956,Poland [2]College of Mathematics,Qingdao University,Qingdao 266071,China

出　　处：《Science China Mathematics》2012年第10期2081-2093,共13页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No. 10871106)

摘　　要：A finite group G is called exceptional if for a Galois extension F/k of number fields with the Galois group G,in the Brauer-Kuroda relation of the Dedekind zeta functions of fields between k and F,the zeta function of F does not appear.In the present paper we describe effectively all exceptional groups of orders divisible by exactly two prime numbers p and q,which have unique subgroups of orders p and q.A finite group G is called exceptional if for a Galois extension F/k of number fields with the Galois group G, in the Brauer-Kuroda relation of the Dedekind zeta functions of fields between k and F, the zeta function of F does not appear. In the present paper we describe effectively all exceptional groups of orders divisible by exactly two prime numbers p and q, which have unique subgroups of orders p and q.

关 键 词：Brauer-Kuroda relation exceptional group pq-group 

分 类 号：O152.1[理学—数学]