Abstract
Let K/Q be any abelian extension where Q is the field of rational numbers. By Galois theory and the Frobenius formula for induced characters, we prove that there exists a metabelian group G and an irreducible character χ of G such that K = Q(χ).
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References
Hungerford T W. Algebra(GTM 73) [M]. New York: Springer-Verlag, 1974.
Joyner D. Arithmetic of Characters of Generalized Symmetric Groups [J]. Arch Math, 2003, 81(1):113–120.
Benard M. Schur Indices and Splitting Fields of the Unitary Groups [J]. J Algebra, 1976, 38(3):318–342.
Fripertinger H. Enumeration of Isometry Classes of Linear (n, k)-Codes over GF(q) in SYMMETRICA [J]. Bayreuth Math Schr, 1995, 49(2):215–223.
Joyner D. Adventures in Group Theory [M]. Baltimore: Johns Hopkins University Press, 2002.
James D, Kerber A. The Representation Theory of the Symmetric Group [M]. Massachusetts: Addison-Wesley, 1981.
Robinson D. A Course in the Theory of Groups (GTM 80) [M]. New York: Springer-Verlag, 1996.
Serre J P. Linear Representations of Finite Groups [M]. New York: Springer-Verlag, 1977.
Isaacs I M. Character Theory of Finite Groups [M]. New York: Dover Press, 1976.
Morandi P. Field and Galois Theory (GTM 167) [M]. New York: Springer-Verlag, 1996.
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Foundation item: Supported by the National Program for the Basic Science Researches of China(G19990751)
Biography: YU Chuxiong(1973–), male, Ph.D. candidate,Lecturer of Jianghan University, research direction:groups and representations.
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Yu, C., Fan, Y. A note on abelian extensions. Wuhan Univ. J. Nat. Sci. 13, 6–8 (2008). https://doi.org/10.1007/s11859-008-0102-8
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DOI: https://doi.org/10.1007/s11859-008-0102-8