On Exceptions in the Brauer–Kuroda Relations

• Autorzy: Browkin J. , Brzeziński J. , Xu K.

Identyfikatory

DOI

10.4064/ba59-3-3

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

exceptional groups; Brauer-Kuroda relations

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2011
• Tom: Vol. 59, no 3
• Strony: 207--214
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Browkin J.

• Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 PL-00-956 Warszawa, Poland

autor

Brzeziński J.

• Mathematical Sciences Chalmers University of Technology and the University of Gothenburg S-41296 Göteborg, Sweden

autor

Xu K.

• College of Mathematics Qingdao University Qingdao 266071, China

Bibliografia

• [B] R. Brauer, Beziehungen zwischen Klassenzahlen von Teilkörpern eines galoisschen Körpers, Math. Nachr. 4 (1951), 158{174.
• [G] D. Gorenstein, Finite Groups, Harper and Row, New York, 1968.
• [K] S. Kuroda, Über die Klassenzahlen algebraischer Zahlkörper, Nagoya Math. J. 1 (1950), 1{10.
• [KS] H. Kurzweil and B. Stellmacher, The Theory of Finite Groups, An Introduction, Springer, New York, 2004.