Abstract
<p>A finite group is called exceptional if for a Galois extension of number fields with the Galois groups , the zeta function of between and does not appear in the Brauer-Kuroda relation of the Dedekind zeta functions. Furthermore, a finite group is called very exceptional if its nontrivial subgroups are all exceptional. In this paper，a Nilpotent group is very exceptional if and only if it has a unique subgroup of prime order for each divisor of .</p>
Publisher
Trans Tech Publications, Ltd.
Reference4 articles.
1. Hall M Jr. The Theory of Groups. New York: The Macmillan Company, (1959).
2. Xu Ming yao and Qu Hai peng , in: Finite groups, edited by Peking University Press(2010).
3. Browkin Jerzy, Brzezinski Juliusz and Xu Kejian, On exceptions in the Brauer-Kuroda relations, Bull. Polish Academy of Sciences, Mathematics, Vol. 59, No. 3, 2011, 207-214.
4. Xu Ming yao, in: Introduction of finite groups, edited by Science Press(2007).