On Exceptions in the Brauer–Kuroda Relations

Volume 59 / 2011

Jerzy Browkin, Juliusz Brzeziński, Kejian Xu Bulletin Polish Acad. Sci. Math. 59 (2011), 207-214 MSC: Primary 20D15; Secondary 11R42. DOI: 10.4064/ba59-3-3


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.


  • Jerzy BrowkinInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    PL-00-956 Warszawa, Poland
  • Juliusz BrzezińskiMathematical Sciences
    Chalmers University of Technology
    and the University of Gothenburg
    S-41296 Göteborg, Sweden
  • Kejian XuCollege of Mathematics
    Qingdao University
    Qingdao 266071, China

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