Finite groups with trivial class groups

Shizuo ENDO; Yumiko HIRONAKA

doi:10.2969/jmsj/03110161

Shizuo ENDO, Yumiko HIRONAKA

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ジャーナルフリー

1979 年 31 巻 1 号 p. 161-174

DOI https://doi.org/10.2969/jmsj/03110161

詳細

Published: 1979 Received: 1977/07/14 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) P. Cassou-Noguès, Classes d'idéaux de l'algèbre d'un groupe abélien, C. R. Acad. Sci. Paris, 276 (1973), A973-A975. (Doctorat de Spécialité, Bordeaux, 1972).
2) P. Cassou-Noguès, Groupe de classes de l'algèbre d'un groupe métacyclique, J. Algebra, 41 (1976), 116-136.
3) A Fröhlich, Module invariants and root numbers for quaternion fields of degree 4l^r, Proc. Cambridge Philos. Soc., 76 (1974), 393-399.
4) A. Fröhlich, M. E. Keating and S. M. J. Wilson, The class group of quaternion and dihedral 2-groups, Mathematika, 21 (1974), 64-71.
5) D. Gorenstein, Finite groups, Harper & Row Publ., New York, 1968.
6) H. Hasse, Über die Klassenzahl abelscher Zahlkörper, Akademie Verlag, Berlin, 1952.
7) M. E. Keating, Class groups of metacyclic groups of order p^r q, p a regular prime, Mathematika, 21 (1974), 90-95.
8) T.Y. Lam, Artin exponent of finite groups, J. Algebra, 9 (1968), 94-119.
9) M. P. Lee, Integral representations of dihedral groups of order 2p, Trans. Amer. Math. Soc., 110 (1964), 213-231.
10) J. Milnor, Introduction to algebraic K-theory, Ann. of Math. Studies, Princeton Univ. Press, Princeton, 1971.
11) I. Reiner and S. Ullom, A Mayer-Vietoris sequence for class groups, J. Algebra, 31 (1974), 305-342.
12) M. Suzuki, On finite groups with cyclic Sylow subgroups for all odd primes, Amer. J. Math., 77 (1955), 657-691.
13) R.G. Swan, Periodic resolutions for finite groups, Ann. of Math., 72 (1960), 267-291.
14) S. Ullom, Nontrivial lower bounds for class groups of integral group rings, Illinois J. Math., 20 (1976), 361-371.

Right : [1] P. Cassou-Noguès, Classes d'idéaux de l'algèbre d'un groupe abélien, C. R. Acad. Sci. Paris, 276 (1973), A973-A975. (Doctorat de Spécialité, Bordeaux, 1972).
[2] P. Cassou-Noguès, Groupe de classes de l'algèbre d'un groupe métacyclique, J. Algebra, 41 (1976), 116-136.
[3] A Fröhlich, Module invariants and root numbers for quaternion fields of degree 4l^r, Proc. Cambridge Philos. Soc., 76 (1974), 393-399.
[4] A. Fröhlich, M. E. Keating and S. M. J. Wilson, The class group of quaternion and dihedral 2-groups, Mathematika, 21 (1974), 64-71.
[5] D. Gorenstein, Finite groups, Harper & Row Publ., New York, 1968.
[6] H. Hasse, Über die Klassenzahl abelscher Zahlkörper, Akademie Verlag, Berlin, 1952.
[7] M. E. Keating, Class groups of metacyclic groups of order p^r q, p a regular prime, Mathematika, 21 (1974), 90-95.
[8] T. Y. Lam, Artin exponent of finite groups, J. Algebra, 9 (1968), 94-119.
[9] M. P. Lee, Integral representations of dihedral groups of order 2p, Trans. Amer. Math. Soc., 110 (1964), 213-231.
[10] J. Milnor, Introduction to algebraic K-theory, Ann. of Math. Studies, Princeton Univ. Press, Princeton, 1971.
[11] I. Reiner and S. Ullom, A Mayer-Vietoris sequence for class groups, J. Algebra, 31 (1974), 305-342.
[12] M. Suzuki, On finite groups with cyclic Sylow subgroups for all odd primes, Amer. J. Math., 77 (1955), 657-691.
[13] R. G. Swan, Periodic resolutions for finite groups, Ann. of Math., 72 (1960), 267-291.
[14] S. Ullom, Nontrivial lower bounds for class groups of integral group rings, Illinois J. Math., 20 (1976), 361-371.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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