Norm exponents and representation groups
HTML articles powered by AMS MathViewer
- by Hans Opolka PDF
- Proc. Amer. Math. Soc. 111 (1991), 595-597 Request permission
Abstract:
This note provides an upper bound for the exponent of the norm residue group ${k^ * }/{\text {Nor}}{{\text {m}}_{K/k}}({K^ * })$ of a finite Galois extension $K/k$ of number fields that depends on the obstruction to the Hasse norm principle for $K/k$ and on a group theoretical constant.References
- E. Artin and J. Tate, Class field theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0223335
- J. W. S. Cassels and A. Fröhlich (eds.), Algebraic number theory, Academic Press, London; Thompson Book Co., Inc., Washington, D.C., 1967. MR 0215665
- Klaus Hoechsmann, Zum Einbettungsproblem, J. Reine Angew. Math. 229 (1968), 81–106 (German). MR 244190, DOI 10.1515/crll.1968.229.81
- W. Hürlimann and D. Saltman, On the exponent of norm residue groups, Proc. Amer. Math. Soc. 93 (1985), no. 3, 417–419. MR 773993, DOI 10.1090/S0002-9939-1985-0773993-2
- B. Huppert, Endliche Gruppen. I, Die Grundlehren der mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703
- Hans Opolka, Zur Auflösung zahlentheoretischer Knoten, Math. Z. 173 (1980), no. 1, 95–103 (German). MR 584351, DOI 10.1007/BF01215526
- Hans Opolka, The norm exponent in Galois extensions of number fields, Proc. Amer. Math. Soc. 99 (1987), no. 1, 41–43. MR 866426, DOI 10.1090/S0002-9939-1987-0866426-0 G. Steinke, Über Auflösungen zahlentheoretischer Knoten, Schriftenreihe Math. Inst. Univ. Münster, Ser. 2, Heft 25, 1982. H. Suzuki, On a central solution of the number knot of a finite $p$-extension of nilpotent class $\leq p - 1$, preprint, 1988.
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 111 (1991), 595-597
- MSC: Primary 11R37; Secondary 11R32, 11R34
- DOI: https://doi.org/10.1090/S0002-9939-1991-1047006-4
- MathSciNet review: 1047006