Very Exceptional Group

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>