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On Exceptions in the Brauer-Kuroda Relations

Jerzy Browkin, Juliusz Brzeziński, Kejian Xu (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

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...

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