Zapiski Nauchnykh Seminarov POMI, Rings and modules, Tome 64 (1976), pp. 49-54
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Z. I. Borevich; B. A. Tolasov. Normal net subgroups of the full linear group. Zapiski Nauchnykh Seminarov POMI, Rings and modules, Tome 64 (1976), pp. 49-54. http://geodesic.mathdoc.fr/item/ZNSL_1976_64_a3/
@article{ZNSL_1976_64_a3,
author = {Z. I. Borevich and B. A. Tolasov},
title = {Normal net subgroups of the full linear group},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {49--54},
year = {1976},
volume = {64},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_64_a3/}
}
TY - JOUR
AU - Z. I. Borevich
AU - B. A. Tolasov
TI - Normal net subgroups of the full linear group
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1976
SP - 49
EP - 54
VL - 64
UR - http://geodesic.mathdoc.fr/item/ZNSL_1976_64_a3/
LA - ru
ID - ZNSL_1976_64_a3
ER -
%0 Journal Article
%A Z. I. Borevich
%A B. A. Tolasov
%T Normal net subgroups of the full linear group
%J Zapiski Nauchnykh Seminarov POMI
%D 1976
%P 49-54
%V 64
%U http://geodesic.mathdoc.fr/item/ZNSL_1976_64_a3/
%G ru
%F ZNSL_1976_64_a3
We prove that for $n\geqslant3$ a net subgroup of the full linear group $G=GL(n,\Lambda)$ over an arbitrary associative ring $\Lambda$ with unity (see [1]) is normal in $G$ if and only if it is a principal congruence subgroup. We also study the case $n=2$, where the situation is, in general, more complicated.
