Geodesic
Improved stability for odd-dimensional orthogonal group
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 25, Tome 414 (2013), pp. 181-192

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For a commutative ring $R$ satisfying the condition $\mathrm{sr}(R)\leq n$ and a root system $\Phi_l$ of type $B_n$ or $C_n$ we compute the kernel of the stabilization map $\mathrm K_1(\Phi_n,R)\to\mathrm K_1(\Phi_{n+1},R)$. 
@article{ZNSL_2013_414_a10,
     author = {S. Sinchuk},
     title = {Improved stability for odd-dimensional orthogonal group},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {181--192},
     publisher = {mathdoc},
     volume = {414},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_414_a10/}
}
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S. Sinchuk. Improved stability for odd-dimensional orthogonal group. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 25, Tome 414 (2013), pp. 181-192. http://geodesic.mathdoc.fr/item/ZNSL_2013_414_a10/