Geodesic
Homological stabilization for the symplectic and orthogonal groups
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 8, Tome 160 (1987), pp. 222-228

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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 $n\geq2p+\dim X$. Here $\dim X$ is the Krull $\dim X$-dimension of the spectrum of the maximal ideals of the ring $R$. 
@article{ZNSL_1987_160_a20,
     author = {I. A. Panin},
     title = {Homological stabilization for the symplectic and orthogonal groups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {222--228},
     publisher = {mathdoc},
     volume = {160},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_160_a20/}
}
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I. A. Panin. Homological stabilization for the symplectic and orthogonal groups. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 8, Tome 160 (1987), pp. 222-228. http://geodesic.mathdoc.fr/item/ZNSL_1987_160_a20/