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On Exceptions in the Brauer–Kuroda Relations

Browkin J., Brzeziński J., Xu K.

Bulletin of the Polish Academy of Sciences. Mathematics

2011

Vol. 59, no 3

207--214

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.

Büchi sequences in local fields and local rings

Browkin J.

Bulletin of the Polish Academy of Sciences. Mathematics

2010

Vol. 58, no 2

109-115

We prove that there exist infinite Büchi sequences in some local rings and local fields, with the exception of the ring Zp of p-adic integers. In Zp there are only finite but arbitrarily long Büchi sequences.

Siódmy problem milenijny : hipoteza Bircha i Swinnertona-Dyera

Browkin J.

Roczniki Polskiego Towarzystwa Matematycznego. Seria 2: Wiadomości Matematyczne

2003

[Z] 39

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