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A simple construction of genus fields of abelian number fields

Author: Xian Ke Zhang
Journal: Proc. Amer. Math. Soc. 94 (1985), 393-395
MSC: Primary 11R20
MathSciNet review: 787879
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Abstract: Simple elementary construction of the genus field $ {K^ * }$ (= maximal abelian subfield of the Hilbert class field) of any abelian number field $ K$ is given without using class field theory. When $ K$ is of type $ (l, \ldots ,l)$ with $ l$ prime, the construction is more explicit. These results contain some former results and show that the main result in [8] has mistakes.

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Keywords: Number field, genus field, abelian extension
Article copyright: © Copyright 1985 American Mathematical Society