Geodesic
The group $SK_2$ for quaternion algebras
Izvestiya. Mathematics , Tome 32 (1989) no. 2, pp. 313-337

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The injectivity of the reduced norm homomorphism $K_2(D)\to K_2(F)$ for the quaternion algebra $D=\binom{a,b}F$, defined over a field $F$ of characteristic $\ne2$, is proved. It is proved that the group $K_2(D)$ can be identified with the subgroup of $K_2(F)$ consisting of all $u$ such that the product $u\cdot\{a,b\}$ is divisible by $2$ in the Milnor group $K_4^M(F)$. Bibliography: 21 titles. 
@article{IM2_1989_32_2_a3,
     author = {A. S. Merkur'ev},
     title = {The group $SK_2$ for quaternion algebras},
     journal = {Izvestiya. Mathematics },
     pages = {313--337},
     publisher = {mathdoc},
     volume = {32},
     number = {2},
     year = {1989},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1989_32_2_a3/}
}
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A. S. Merkur'ev. The group $SK_2$ for quaternion algebras. Izvestiya. Mathematics , Tome 32 (1989) no. 2, pp. 313-337. http://geodesic.mathdoc.fr/item/IM2_1989_32_2_a3/