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Integral representations with trivial first cohomology groups

Published online by Cambridge University Press:  22 January 2016

Shizuo Endo  and
Takehiko Miyata
Shizuo Endo
Affiliation:
Department of Mathematics, Tokyo Metropolitan University Fukazaiua, Setagaya-ku, Tokyo, Japan
Takehiko Miyata
Affiliation:
Department of Mathematics Osaka City, University Sugimoto, Sumiyoshi-ku Osaka-shi, Japan
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Let Π be a finite group and denote by MΠ the class of finitely generated Z-free ZΠ-modules. In [2] we defined a certain equivalence relation on MΠ and constructed the abelian semigroup T(Π), which was studied in [3] (see [1] and [5], too).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 85 , March 1982 , pp. 231 - 240
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

References

[ 1 ] Colliot-Thélène, J.-L. et Sansuc, J.-J., La R-équivalence sur les tores, Ann. Sci. Éc. Norm. Sup., 10 (1977), 175–230.CrossRefGoogle Scholar
[ 2 ] Endo, S. and Miyata, T., Quasi-permutation modules over finite groups, J. Math. Soc. Japan, 25 (1973), 397–421: II, ibid., 26 (1974), 698–713.CrossRefGoogle Scholar
[ 3 ] Endo, S. and Miyata, T., On a classification of the function fields of algebraic tori, Nagoya Math. J., 56 (1975), 85–104; Corrigendum, ibid., 79 (1980), 187–190.CrossRefGoogle Scholar
[ 4 ] Endo, S. and Miyata, T., On integral representations of finite groups, Sugaku, 27 (1975), 232-240 (Japanese).Google Scholar
[ 5 ] Voskresenskiĭ, V.E., Stable equivalence of algebraic tori, Izv. Akad. Nauk SSSR, 38 (1974), 3–10.Google Scholar