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St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

ISSN 1547-7371 (online) ISSN 1061-0022 (print)

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.68.

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Elementary subgroup of an isotropic reductive group is perfect
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by A. Yu. Luzgarev and A. K. Stavrova
Translated by: A. Yu. Luzgarev
St. Petersburg Math. J. 23 (2012), 881-890
DOI: https://doi.org/10.1090/S1061-0022-2012-01221-5
Published electronically: July 10, 2012
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Abstract:

Let $G$ be an isotropic reductive algebraic group over a commutative ring $R$. Assume that the elementary subgroup $E(R)$ of the group of points $G(R)$ is well defined. Then $E(R)$ is perfect, except for the well-known case of a split reductive group of type $C_2$ or $G_2$.
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Bibliographic Information
  • A. Yu. Luzgarev
  • Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskaya ul. 28, Stary Petergof, St. Petersburg 198504, Russia
  • Email: mahalex@gmail.com
  • A. K. Stavrova
  • Affiliation: Fakultät für Mathematik, Universität Duisburg-Essen, Germany
  • MR Author ID: 752852
  • Email: anastasia.stavrova@gmail.com
  • Received by editor(s): May 27, 2010
  • Published electronically: July 10, 2012
  • Additional Notes: Supported by the research program 6.38.74.2011 “The Structural Theory and Geometry of Algebraic Groups and Their Applications in Representation Theory and Algebraic K-Theory” of St. Petersburg State University and by the RFBR projects 09-01-00878, 09-01-90304, 10-01-00551, 10-01-90016. The first author was also supported by the RFBR project 09-01-00874. The second author was also supported by the grants DFG GI 706/1-2 and DFG SFB/TR 45.

    • Dedicated: To our Teacher Nikolai Vavilov, on the occasion of his 60th birthday
  • © Copyright 2012 American Mathematical Society
  • Journal: St. Petersburg Math. J. 23 (2012), 881-890
  • MSC (2010): Primary 20G35
  • DOI: https://doi.org/10.1090/S1061-0022-2012-01221-5
  • MathSciNet review: 2918426