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
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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
$$
E(n,S)E(2n,R,A)\leq H\leq N_{\operatorname{GL}(2n,R)}(E(n,S)E(2n,R,A)).
$$
@article{ZNSL_2017_455_a15,
author = {T. N. Hoi and N. H. T. Nhat},
title = {Subgroups of the general linear group containing the elementary subgroup over a~commutative ring extension of rank~2},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {209--225},
publisher = {mathdoc},
volume = {455},
year = {2017},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a15/}
}
TY - JOUR AU - T. N. Hoi AU - N. H. T. Nhat TI - Subgroups of the general linear group containing the elementary subgroup over a~commutative ring extension of rank~2 JO - Zapiski Nauchnykh Seminarov POMI PY - 2017 SP - 209 EP - 225 VL - 455 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a15/ LA - en ID - ZNSL_2017_455_a15 ER -
%0 Journal Article %A T. N. Hoi %A N. H. T. Nhat %T Subgroups of the general linear group containing the elementary subgroup over a~commutative ring extension of rank~2 %J Zapiski Nauchnykh Seminarov POMI %D 2017 %P 209-225 %V 455 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a15/ %G en %F ZNSL_2017_455_a15
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/