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This article is cited in 5 scientific papers (total in 6 papers)
Class numbers and groups of algebraic groups
V. P. Platonov, A. A. Bondarenko, A. S. Rapinchuk
Abstract:
The class number of an algebraic group $G$ defined over a global field is the number of double cosets of the adele group $G_A$ with respect to the subgroups of integral and principal adeles. In most cases the set of double cosets has the natural structure of an abelian group, called the class group of $G$. In this article the class number of a semisimple group $G$ is computed, and it is proved that any finite abelian group can be realized as a class group.
Bibliography: 24 titles.
Received: 03.01.1979
Citation:
V. P. Platonov, A. A. Bondarenko, A. S. Rapinchuk, “Class numbers and groups of algebraic groups”, Izv. Akad. Nauk SSSR Ser. Mat., 43:3 (1979), 603–627; Math. USSR-Izv., 14:3 (1980), 547–569
Linking options:
https://www.mathnet.ru/eng/im1724https://doi.org/10.1070/IM1980v014n03ABEH001144 https://www.mathnet.ru/eng/im/v43/i3/p603
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Abstract page: | 420 | Russian version PDF: | 89 | English version PDF: | 8 | References: | 48 | First page: | 3 |
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