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Izv. Akad. Nauk SSSR Ser. Mat., 1979, Volume 43, Issue 3, Pages 603–627 (Mi izv1724)  

This article is cited in 4 scientific papers (total in 5 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.

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English version:
Mathematics of the USSR-Izvestiya, 1980, 14:3, 547–569

Bibliographic databases:

UDC: 513.6
MSC: Primary 20G25, 20G30; Secondary 10C30
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

Citation in format AMSBIB
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\by V.~P.~Platonov, A.~A.~Bondarenko, A.~S.~Rapinchuk
\paper Class numbers and groups of algebraic groups
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1979
\vol 43
\issue 3
\pages 603--627
\mathnet{http://mi.mathnet.ru/izv1724}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=541661}
\zmath{https://zbmath.org/?q=an:0448.20045}
\transl
\jour Math. USSR-Izv.
\yr 1980
\vol 14
\issue 3
\pages 547--569
\crossref{https://doi.org/10.1070/IM1980v014n03ABEH001144}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980KN98400003}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. P. Platonov, A. A. Bondarenko, A. S. Rapinchuk, “Class numbers and groups of algebraic groups. II”, Math. USSR-Izv., 16:2 (1981), 357–372  mathnet  crossref  mathscinet  zmath  isi
    2. R. A. Sarkisyan, “Algorithmic questions for linear algebraic groups. I”, Math. USSR-Sb., 41:2 (1982), 149–179  mathnet  crossref  mathscinet  zmath
    3. A. S. Rapinchuk, “Class numbers in the genus of quadratic forms, and algebraic groups”, Math. USSR-Izv., 19:1 (1982), 79–93  mathnet  crossref  mathscinet  zmath
    4. V. P. Platonov, “The arithmetic theory of algebraic groups”, Russian Math. Surveys, 37:3 (1982), 1–62  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. S. I. Adian, E. I. Zel'manov, G. A. Margulis, S. P. Novikov, A. S. Rapinchuk, L. D. Faddeev, V. I. Yanchevskii, “Vladimir Petrovich Platonov (on his 60th birthday)”, Russian Math. Surveys, 55:3 (2000), 601–610  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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