On Exceptions in the Brauer-Kuroda Relations

Jerzy Browkin, Juliusz Brzeziński, and Kejian Xu. "On Exceptions in the Brauer-Kuroda Relations." Bulletin of the Polish Academy of Sciences. Mathematics 59.3 (2011): 207-214. <http://eudml.org/doc/281264>.

@article{JerzyBrowkin2011,
abstract = {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.},
author = {Jerzy Browkin, Juliusz Brzeziński, Kejian Xu},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {Brauer relations; class number relations; Dedekind zeta function; finite groups; nilpotent exceptional groups},
language = {eng},
number = {3},
pages = {207-214},
title = {On Exceptions in the Brauer-Kuroda Relations},
url = {http://eudml.org/doc/281264},
volume = {59},
year = {2011},
}

TY - JOUR
AU - Jerzy Browkin
AU - Juliusz Brzeziński
AU - Kejian Xu
TI - On Exceptions in the Brauer-Kuroda Relations
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2011
VL - 59
IS - 3
SP - 207
EP - 214
AB - 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.
LA - eng
KW - Brauer relations; class number relations; Dedekind zeta function; finite groups; nilpotent exceptional groups
UR - http://eudml.org/doc/281264
ER -