On Exceptions in the Brauer–Kuroda Relations
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) no. 3, pp. 207-214
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
galois extension number field galois group brauer kuroda theorem gives expression dedekind zeta function field product zeta functions its subfields containing provided group exceptional paper investigate exceptional groups particular determine nilpotent exceptional groups sufficient condition group exceptional many examples nonnilpotent solvable nonsolvable exceptional groups
Affiliations des auteurs :
Jerzy Browkin 1 ; Juliusz Brzeziński 2 ; Kejian Xu 3
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author = {Jerzy Browkin and Juliusz Brzezi\'nski and Kejian Xu},
title = {On {Exceptions} in the {Brauer{\textendash}Kuroda} {Relations}},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
pages = {207--214},
publisher = {mathdoc},
volume = {59},
number = {3},
year = {2011},
doi = {10.4064/ba59-3-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ba59-3-3/}
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Jerzy Browkin; Juliusz Brzeziński; Kejian Xu. On Exceptions in the Brauer–Kuroda Relations. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) no. 3, pp. 207-214. doi: 10.4064/ba59-3-3
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