Geodesic
On Exceptions in the Brauer–Kuroda Relations
Jerzy Browkin 1   ; Juliusz Brzeziński 2   ; Kejian Xu 3
1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 PL-00-956 Warszawa, Poland
2 Mathematical Sciences Chalmers University of Technology and the University of Gothenburg S-41296 Göteborg, Sweden
3 College of Mathematics Qingdao University Qingdao 266071, China
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) no. 3, pp. 207-214 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ba59-3-3
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

Jerzy Browkin  1   ; Juliusz Brzeziński  2   ; Kejian Xu  3

1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 PL-00-956 Warszawa, Poland
2 Mathematical Sciences Chalmers University of Technology and the University of Gothenburg S-41296 Göteborg, Sweden
3 College of Mathematics Qingdao University Qingdao 266071, China 
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     title = {On {Exceptions} in the {Brauer{\textendash}Kuroda} {Relations}},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
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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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