Geodesic
$K_1$-theory and the congruence problem
Matematičeskie zametki, Tome 5 (1969) no. 2, pp. 233-244

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The following results are presented: a) A $K_1$-functor of a noncommutative ring with unity is a factor of a general linear group with respect to the subgroup of elementary matrices; b) a description is given of all the subgroups of finite index in a special linear group over the order in a field. 
@article{MZM_1969_5_2_a10,
     author = {L. N. Vaserstein},
     title = {$K_1$-theory and the congruence problem},
     journal = {Matemati\v{c}eskie zametki},
     pages = {233--244},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_5_2_a10/}
}
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L. N. Vaserstein. $K_1$-theory and the congruence problem. Matematičeskie zametki, Tome 5 (1969) no. 2, pp. 233-244. http://geodesic.mathdoc.fr/item/MZM_1969_5_2_a10/