Abstract: | We study the subgroups of the full linear group GL(n, R) over a Dedekind ring R that contain the group of quasidiagonal matrices of fixed type with diagonal blocks of at least third order, each of which is generated by elementary matrices. For any such subgroup H there exists a unique D-net of ideals of R such that, where E( ) is the subgroup generated by all transvections of the net subgroup G( ). and is the normalizer of G( ). The subgroup E( ) is normal in. To study the factor group we introduce an intermediate subgroup F( ), E( ) F( ) G( ). The group is finite and is connected with permutations in the symmetric group. The factor group G( )/F( ) is Abelian — these are the values of a certain determinant. In the calculation of F( )/E( ) appears the SK1-functor. Results are stated without proof.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 94, pp. 13–20, 1979. |