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Overgroups of elementary symplectic groups


Authors: N. A. Vavilov and V. A. Petrov
Translated by: the authors
Original publication: Algebra i Analiz, tom 15 (2003), nomer 4.
Journal: St. Petersburg Math. J. 15 (2004), 515-543
MSC (2000): Primary 20G35
DOI: https://doi.org/10.1090/S1061-0022-04-00820-9
Published electronically: July 6, 2004
MathSciNet review: 2068980
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Abstract: Let $R$ be a commutative ring, and let $l\ge 2$; for $l=2$ it is assumed additionally that $R$ has no residue fields of two elements. The subgroups of the general linear group $\operatorname{GL}(n,R)$ that contain the elementary symplectic group $\operatorname{Ep}(2l,R)$ are described. In the case where $R=K$ is a field, similar results were obtained earlier by Dye, King, and Shang Zhi Li.


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Additional Information

N. A. Vavilov
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ Prospekt 28, St. Petersburg, 198504, Russia

V. A. Petrov
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ Prospekt 28, St. Petersburg 198504, Russia

DOI: https://doi.org/10.1090/S1061-0022-04-00820-9
Received by editor(s): February 18, 2003
Published electronically: July 6, 2004
Additional Notes: The present paper has been written in the framework of the RFBR projects nos. 01-01-00924 and 00-01-00441, and INTAS 00-566. The theorem on decomposition of unipotents mentioned in §13 is a part of first author’s joint work with A. Bak and was carried out at the University of Bielefeld with the support of AvH-Stiftung, SFB-343, and INTAS 93-436. At the final stage, the work of the authors was supported by express grants of the Russian Ministry of Higher Education ‘Geometry of root subgroups’ PD02-1.1-371 and ‘Overgroups of semisimple groups’ E02-1.0-61.
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