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Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 2, Pages 398–410 (Mi izv1247)  

This article is cited in 3 scientific papers (total in 3 papers)

On projective simplicity of certain groups of rational points over algebraic number fields

V. I. Chernousov


Abstract: It is proved that, if $G$ is a simply connected anisotropic absolutely simple algebraic group with rank $n\geqslant2$ defined over an algebraic number field and decomposable over a quadratic extension, then the group $G(K)$ of rational points is projectively simple, i.e. the factor group modulo the center is simple. Projective simplicity of algebraic groups of type $B_n$, $C_n$, $G_2$, $F_4$, $F_7$ is obtained as a corollary, and also the same for groups of type $E_8$ whenever the Hasse principle holds. In addition the problem of projective simplicity for groups of type $^{(1)}D_n$, $^{(2)}D_n$ ($n\geqslant4$) is reduced to the case of groups of type $A_3$.
Bibliography: 18 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1990, 34:2, 409–423

Bibliographic databases:

UDC: 512.7
MSC: Primary 20G30; Secondary 15A66, 11E88, 11E57, 20G20
Received: 06.05.1987

Citation: V. I. Chernousov, “On projective simplicity of certain groups of rational points over algebraic number fields”, Izv. Akad. Nauk SSSR Ser. Mat., 53:2 (1989), 398–410; Math. USSR-Izv., 34:2 (1990), 409–423

Citation in format AMSBIB
\Bibitem{Che89}
\by V.~I.~Chernousov
\paper On projective simplicity of certain groups of rational points over algebraic number fields
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 2
\pages 398--410
\mathnet{http://mi.mathnet.ru/izv1247}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=998303}
\zmath{https://zbmath.org/?q=an:0703.14014}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 34
\issue 2
\pages 409--423
\crossref{https://doi.org/10.1070/IM1990v034n02ABEH000657}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. G. M. Tomanov, “On the structure of division algebras of index $2^m$”, Russian Math. Surveys, 45:6 (1990), 170–172  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. G. M. Tomanov, “On the group of reduced norm 1 group of a division algebra over a global field”, Math. USSR-Izv., 39:1 (1992), 895–904  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. M. S. Raghunathan, “The congruence subgroup problem”, Proc Math Sci, 114:4 (2004), 299  crossref  mathscinet  zmath
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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