Overgroups of elementary symplectic groups

Vavilov, N.; Petrov, V.

doi:10.1090/S1061-0022-04-00820-9

Overgroups of elementary symplectic groups
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by N. A. Vavilov and V. A. Petrov
Translated by: the authors

St. Petersburg Math. J. 15 (2004), 515-543

DOI: https://doi.org/10.1090/S1061-0022-04-00820-9

Published electronically: July 6, 2004

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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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