A note on abelian extensions |
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| Authors: | Chuxiong Yu Yun Fan |
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| Affiliation: | (1) School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, Hubei, China;(2) School of Mathematics and Computer Science, Jianghan University, Wuhan, 430056, Hubei, China;(3) School of Mathematics and Statistics, Huazhong Normal University, Wuhan, 430079, Hubei, China |
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| 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). Biography: YU Chuxiong(1973–), male, Ph.D. candidate,Lecturer of Jianghan University, research direction:groups and representations. |
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| Keywords: | abelian extensions metabelian groups induced characters Galois groups |
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