Geodesic
Normal net subgroups of the full linear group
Zapiski Nauchnykh Seminarov POMI, Rings and modules, Tome 64 (1976), pp. 49-54

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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. 
@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},
     publisher = {mathdoc},
     volume = {64},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_64_a3/}
}
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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/