Geodesic
Subgroups of the general linear group containing the elementary subgroup over a commutative ring extension of rank 2
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 31, Tome 455 (2017), pp. 209-225 
T. N. Hoi; N. H. T. Nhat. Subgroups of the general linear group containing the elementary subgroup over a commutative ring extension of rank 2. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 31, Tome 455 (2017), pp. 209-225. http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a15/
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     title = {Subgroups of the general linear group containing the elementary subgroup over a~commutative ring extension of rank~2},
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}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $R=\prod_{i\in I}F_i$ be a direct product of fields and let $S=R[\sqrt d]=\prod_{i\in I}F_i[\sqrt{d_i}]$ be a ring extension of rank 2 of $R$. The subgroups of the general linear group $\operatorname{GL}(2n,R)$, $n\geq3$ that contain the elementary group $E(n,S)$ are described. It is shown that for every such a subgroup $H$ there exists a unique ideal $A\unlhd R$ such that $$ E(n,S)E(2n,R,A)\leq H\leq N_{\operatorname{GL}(2n,R)}(E(n,S)E(2n,R,A)). $$

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