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On unramified cyclic extensions of degree l of algebraic number fields of degree l

Published online by Cambridge University Press:  22 January 2016

Yoshitaka Odai
Yoshitaka Odai*
Affiliation:
Department of Mathematics, Faculty of Science Tokyo Metropolitan University, Fukasawa Setagaya-ku, Tokyo, 158
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Let I be an odd prime number and let K be an algebraic number field of degree I. Let M denote the genus field of K, i.e., the maximal extension of K which is a composite of an absolute abelian number field with K and is unramified at all the finite primes of K. In [4] Ishida has explicitly constructed M. Therefore it is of some interest to investigate unramified cyclic extensions of K of degree l, which are not contained in M. In the preceding paper [6] we have obtained some results about this problem in the case that K is a pure cubic field. The purpose of this paper is to extend those results.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 107 , September 1987 , pp. 135 - 146
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1987

References

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