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This article is cited in 3 scientific papers (total in 4 papers)
Class numbers and groups of algebraic groups. II
V. P. Platonov, A. A. Bondarenko, A. S. Rapinchuk
Abstract:
The central result of this article is a realization theorem, according to which, for a semisimple indefinite algebraic $K$-group $G$ ($K$ is an algebraic number field) an arbitrary finite abelian group of exponent $f$, where $f$ is the index of the kernel $F$ of the universal covering $\widetilde G\to G$, can be realized as a class group $\mathscr G\operatorname{cl}(\varphi(G))$.
In the second part of the article the class number of semisimple groups that are not indefinite (groups of compact type) is investigated. The following general theorem is proved: if $G$ is a semisimple group of compact type of degree $n$, then for any natural number $r$ there exists a lattice $M(r)\subset K^{2n}$ such that $\operatorname{cl}(G^{M(r)})$ is divisible by $r$.
Bibliography: 12 titles.
Received: 13.11.1979
Citation:
V. P. Platonov, A. A. Bondarenko, A. S. Rapinchuk, “Class numbers and groups of algebraic groups. II”, Izv. Akad. Nauk SSSR Ser. Mat., 44:2 (1980), 395–414; Math. USSR-Izv., 16:2 (1981), 357–372
Linking options:
https://www.mathnet.ru/eng/im1671https://doi.org/10.1070/IM1981v016n02ABEH001312 https://www.mathnet.ru/eng/im/v44/i2/p395
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Abstract page: | 422 | Russian version PDF: | 102 | English version PDF: | 10 | References: | 51 | First page: | 3 |
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