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Some Remarks to Ono’s theorem on a generalization of Gauss’ genus theory

Published online by Cambridge University Press:  22 January 2016

Ryuji Sasaki
Ryuji Sasaki*
Affiliation:
Department of Mathematics, College of Science and Technology, Nihon University Surugadai, Tokyo 101, Japan
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Let K\k be a finite Galois extension of finite algebraic number fields with Galois group g. We denote by Gm the multiplicative group defined over the rational number field Q and put

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Type
Research Article
Information
Nagoya Mathematical Journal , Volume 111 , September 1988 , pp. 131 - 142
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1988

References

[1] Cassels, J. W. S. and Fröhlich, A., Algebraic number theory, Academic Press, 1976.Google Scholar
[2] Gras, G., Sur les 1-classes d’ideaux dans les extensions cycliques relatives de degree premier 1, Ann. Inst. Fourier, Grenoble, 23 (1973), 1–48.Google Scholar
[3] Ono, T., Arithmetic of algebraic tori, Ann. of Math., 74 (1961), 101–139.Google Scholar
[4] Ono, T., On the Tamagawa number of algebraic tori, Ann. of Math., 78 (1963), 47–73.Google Scholar
[5] Ono, T., Arithmetic of algebraic groups and its applications, Lecture note at St. Paul’s University, 1986.Google Scholar
[6] Ono, T., Algebraic groups and number theory (Japanese), Sugaku 38 (1986), 218–231.Google Scholar
[7] Ono, T., On some class number relations for Galois extensions, Nagoya Math. J., 107 (1987), 122–133.Google Scholar
[8] Satake, I., Classification theory of semi-simple algebraic groups, Marcel Dekker, 1971.Google Scholar
[9] Shyr, Jih-Min, On some class number relations of algebraic tori, Michigan Math. J., 24 (1977), 365–377.CrossRefGoogle Scholar
[10] Takagi, T., Theory of algebraic numbers (Japanese), Iwanami, 1971.Google Scholar
[11] Washington, L. C., Introduction to Cyclotomic fields, Springer, 1982.Google Scholar
[12] Weil, A., Adeles and algebraic groups, notes by Demazure, M. and Ono, T., Birkhäuser, 1982.Google Scholar