The stabilization of symplectic groups over a polynomial ring
Sbornik. Mathematics, Tome 34 (1978) no. 5, pp. 655-669 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove that if $B$ is a polynomial ring over a field, then for $r\geqslant2$, any element of $Sp_{2r}B$ can be written as a product of elementary symplectic matrices over $B$. We also prove a stabilization theorem for the symplectic $K_1$-functor in the case of polynomial rings and Laurent rings. Bibliography: 6 titles.
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     title = {The stabilization of symplectic groups over a~polynomial ring},
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V. I. Kopeiko. The stabilization of symplectic groups over a polynomial ring. Sbornik. Mathematics, Tome 34 (1978) no. 5, pp. 655-669. http://geodesic.mathdoc.fr/item/SM_1978_34_5_a5/

[1] X. Base, Algebraicheskaya $K$-teoriya, izd-vo “Mir”, Moskva, 1973 | MR

[2] A. A. Suslin, “O strukture spetsialnoi lineinoi gruppy nad koltsami mnogochlenov”, Izv. AN SSSR, seriya matem., 41 (1977), 503–516 | MR

[3] L. N. Vasershtein, “Stabilizatsiya unitarnykh i ortogonalnykh grupp nad koltsom s involyutsiei”, Matem. sb., 81(123) (1970), 328–351

[4] L. N. Vasershtein, A. A. Suslin, “Problema Serra o proektivnykh modulyakh nad koltsami mnogochlenov i algebraicheskaya $K$-teoriya”, Izv. AN SSSR, seriya matem., 40 (1976), 993–1055

[5] X. Base, Dzh. Milnor, Zh.-P. Serr, “Reshenie kongruents-problemy dlya $SL_n(n\ge 3)$ i $Sp_{2n}(n\ge 2)$”, Matematika, 15:1 (1971), 44–60

[6] Dzh. Milnor, Vvedenie v algebraicheskuyu $K$-teoriyu, izd-vo “Mir”, Moskva, 1974 | MR