Stabilization of unitary and orthogonal groups over a ring with involution
Sbornik. Mathematics, Tome 10 (1970) no. 3, pp. 307-326 Cet article a éte moissonné depuis la source Math-Net.Ru

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Orthogonal and unitary groups over an associative ring with involution are examined. Using these groups, orthogonal and unitary $K_1$-functors are introduced which are similar to general $K_1$-functors associated with a general linear group over a ring. Results are obtained about stabilization of orthogonal and unitary groups. Bibliography: 9 titles.
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     title = {Stabilization of unitary and orthogonal groups over a~ring with involution},
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L. N. Vaserstein. Stabilization of unitary and orthogonal groups over a ring with involution. Sbornik. Mathematics, Tome 10 (1970) no. 3, pp. 307-326. http://geodesic.mathdoc.fr/item/SM_1970_10_3_a1/

[1] H. Bass, “$K$-theory and stable algebra”, Publ. Math., 22 (1964), 5–60 | MR | Zbl

[2] L. N. Vasershtein, “O stabilizatsii dlya obschei lineinoi gruppy nad koltsom”, Matem. sb., 79(121) (1969), 405–424

[3] N. Burbaki, Algebra (moduli, koltsa, formy), Nauka, Moskva, 1956 | MR

[4] H. Bass, Lectures on Topics in Algebraic $K$-theory, Bombay, 1967

[5] L. N. Vasershtein, “$K_1$-teoriya i kongruentsproblema”, Matem. zametki, 5:2 (1969), 233–244

[6] H. Bass, J. Milnor, J.-P. Serre, “Solution of the congruence subgroup problem for $SL_n$ ($n\geqslant3$) and $Sp_{2n}$ ($n\geqslant2$)”, Publ. Math., 33 (1967), 59–137 | MR | Zbl

[7] C. E. Wall, “The structure of a unitary factor group”, Publ. Math., 1 (1959), 5–21 | MR

[8] W. Kligenberg, “Orthogonal Gruppen tiber lokalen Rings”, Amer. J. Math., 83:2 (1961), 281–320 | DOI | MR

[9] W. Kligenberg, “Simplectic groups over local rings”, Amer. J. Math., 83:2 (1963), 232–240 | DOI | MR