Suppose K is a global field, S a finite set of valuations of K containing all Archimedean valuations, and R the ring of S-integral elements of K. Assume that card S≥2, R is generated by its invertible elements, and the ideal of R generated by the differences ε-1 for all invertible e{open} coincides with R. Under these assumptions, the parabolic subgroups of GL(n, R) are described. Namely, for each parabolic subgroup P there exists a unique net b{cyrillic} of ideals of R (Ref. Zh. Mat., 1977, 2A280) such that e(b{cyrillic})≤P≤G(b{cyrillic}), where G is the net subgroup of (b{cyrillic}) and E(b{cyrillic}) is the subgroup generated by the transvections in G(b{cyrillic}). It is shown that E(b{cyrillic}) is a normal subgroup of G(b{cyrillic}). The factor group G(b{cyrillic}/E(b{cyrillic})) is studied. The case of the special linear group is also considered.