Let F be a Galois extension of a number field k with the Galois group G. The Brauer-Kuroda theorem gives an expression of the Dedekind zeta function of the field F as a product of zeta functions of some of its subfields containing k, provided the group G is not exceptional. In this paper, we investigate the exceptional groups. In particular, we determine all nilpotent exceptional groups, and give a sufficient condition for a group to be exceptional. We give many examples of nonnilpotent solvable and nonsolvable exceptional groups.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-3-3,
author = {Jerzy Browkin and Juliusz Brzezi\'nski and Kejian Xu},
title = {On Exceptions in the Brauer-Kuroda Relations},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {59},
year = {2011},
pages = {207-214},
zbl = {1244.20013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-3-3}
}
Jerzy Browkin; Juliusz Brzeziński; Kejian Xu. On Exceptions in the Brauer-Kuroda Relations. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) pp. 207-214. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-3-3/