Homological stabilization for the orthogonal and symplectic groups

It is proved that for a commutative ring R with identity and without finite residue R, fields, the integral groups of homologies Hp(sp_2n(R)) and Hp(O_2n(R)) for a fixed p do not vary with the growth of n only if n⩾2p+dim X Here dim X is the Krull dim X-dimension of the spectrum of the maximal ideals of the ring R. Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 160, pp. 222–228, 1987.