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Mathematics of the USSR-Izvestiya, 1980, Volume 14, Issue 3, Pages 547–569
DOI: https://doi.org/10.1070/IM1980v014n03ABEH001144 (Mi im1724) 		 
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
English version PDF (1117 kB) Citations (6)
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DOI: https://doi.org/10.1070/IM1980v014n03ABEH001144
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
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1979, Volume 43, Issue 3, Pages 603–627
Bibliographic databases:
UDC: 513.6
MSC: Primary 20G25, 20G30; Secondary 10C30
Language: English
Original paper language: Russian
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/im1724}
\mathscinet{http://mathscinet.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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1980KN98400003}
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  • https://doi.org/10.1070/IM1980v014n03ABEH001144
  • https://www.mathnet.ru/eng/im/v43/i3/p603
    Cycle of papers
    This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:420
    Russian version PDF:89
    English version PDF:8
    References:48
    First page:3
     
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