Geodesic
Overgroups of $\mathrm{EO}(2l,R)$
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 7, Tome 272 (2000), pp. 68-85

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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. 
@article{ZNSL_2000_272_a3,
     author = {N. A. Vavilov and V. A. Petrov},
     title = {Overgroups of $\mathrm{EO}(2l,R)$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {68--85},
     publisher = {mathdoc},
     volume = {272},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_272_a3/}
}
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N. A. Vavilov; V. A. Petrov. Overgroups of $\mathrm{EO}(2l,R)$. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 7, Tome 272 (2000), pp. 68-85. http://geodesic.mathdoc.fr/item/ZNSL_2000_272_a3/