Geodesic
Subgroups of linear groups rich in transvections
Zapiski Nauchnykh Seminarov POMI, Rings and linear groups, Tome 75 (1978), pp. 22-31

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $K$ be a field and let $k$ be a subfield of it. Subgroups $H$ in $\mathrm{GL}(n,K)$ are considered which contain all diagonal matrices with nonzero elements in the subfield $k$. It is said that $H$ is rich in transvections if for any pair of indices $i\ne j$ $H$ contains a transvection with a nonzero element in the position $(i,j)$. In the work a description is given of all intermediate subgroups $H$ rich in transvections under the condition that $n\ge3$, $(K:k)\ge3$. A similar question is solved also for the special linear group. Bibl. 5 titles. 
@article{ZNSL_1978_75_a2,
     author = {Z. I. Borevich},
     title = {Subgroups of linear groups rich in transvections},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {22--31},
     publisher = {mathdoc},
     volume = {75},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1978_75_a2/}
}
TY  - JOUR
AU  - Z. I. Borevich
TI  - Subgroups of linear groups rich in transvections
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1978
SP  - 22
EP  - 31
VL  - 75
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1978_75_a2/
LA  - ru
ID  - ZNSL_1978_75_a2
ER  - 
%0 Journal Article
%A Z. I. Borevich
%T Subgroups of linear groups rich in transvections
%J Zapiski Nauchnykh Seminarov POMI
%D 1978
%P 22-31
%V 75
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_1978_75_a2/
%G ru
%F ZNSL_1978_75_a2
Z. I. Borevich. Subgroups of linear groups rich in transvections. Zapiski Nauchnykh Seminarov POMI, Rings and linear groups, Tome 75 (1978), pp. 22-31. http://geodesic.mathdoc.fr/item/ZNSL_1978_75_a2/