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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2000 Volume 272, Pages 68–85 (Mi znsl1363)

This article is cited in 26 papers

Overgroups of $\mathrm{EO}(2l,R)$

N. A. Vavilov, V. A. Petrov

Saint-Petersburg State University

Abstract: Let $R$ be a commutative ring with 1, $2\in R^*$, and $l\ge 3$. We describe subgroups of the general linear group $\mathrm{GL}(n,R)$ containing the split elementary orthogonal group $\mathrm{EO}(2l,R)$. For every intermediate subgroup $H$ there exists a unique maximal ideal $A\unlhd R$ such that $E(2l,R,A)\le H$, and moreover $H$ normalises $\mathrm{EO}(2l,R)E(2l,R,A)$. In the case when $R=K$ is a field, similar results have been obtained earlier by Dye, King, Li Shangzhi and Bashkirov.

UDC: 519.46

Received: 10.06.2000


 English version:
Journal of Mathematical Sciences (New York), 2003, 116:1, 2917–2925

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