| A Note on Abelian Extensions |
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| 作者姓名： | YU Chuxiong FAN Yun |
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| 作者单位： | [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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| 基金项目： | Supported by the National Program for the Basic Science Researches of China（G 19990751） |
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| 摘 要： | 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 X of G such that K=Q（X）.
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| 关 键 词： | 群表示论 亚可换群 数学理论 感应形状 |
| 文章编号： | 1007-1202（2008）01-0006-03 |
| 收稿时间： | 2007-04-10 |
A note on abelian extensions |
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| YU Chuxiong FAN Yun.A Note on Abelian Extensions[J].Wuhan University Journal of Natural Sciences,2008,13(1):6-8. |
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| Authors: | Chuxiong Yu Yun Fan |
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| Institution: | (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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