Normal net subgroups of the full linear group

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.