The problem of strong approximation and the Kneser--Tits conjecture for algebraic groups
Izvestiya. Mathematics , Tome 3 (1969) no. 6, pp. 1139-1147.

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We conclude an investigation of the problem of strong approximation in algebraic groups. A basic role is played by the proof of the Kneser–Tits conjecture concerning simple, simply connected groups over locally compact fields.
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V. P. Platonov. The problem of strong approximation and the Kneser--Tits conjecture for algebraic groups. Izvestiya. Mathematics , Tome 3 (1969) no. 6, pp. 1139-1147. http://geodesic.mathdoc.fr/item/IM2_1969_3_6_a0/

[1] Eichler M., “Allgemeine Kongruenzklassenenteilungen der Ideale einfacher Algebren über algebraischen Zahlkörpern und ihre $L$-Reihen”, J. Reine Angew. Math., 179 (1938), 227–251 | Zbl

[2] Eichler M., Quadratische Formen und ortogonale Gruppen, Berlin, 1952 | MR

[3] Kneser M., “Starke Approximation in algebraischen Gruppen. I”, J. Reine Angew. Math., 218 (1965), 190–203 | MR | Zbl

[4] Kneser M., “Starke Approximation”, Proc. Symp. Pure Math., 9, Providence, 1966, 187–197 | MR

[5] Kneser M., Einfach zusammenhängende algebraische Gruppen in der Arithmetik (Int. Cong. Math.), Stockholm, 1962 | MR

[6] Shimura G., “Arithmetic of unitary groups”, Ann. Math., 79 (1964), 369–409 | DOI | MR | Zbl

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

[8] Platonov V. P., “Gruppy adelei i tselochislennye predstavleniya”, Izv. AN SSSR. Seriya matem., 33 (1969), 155–163 | MR

[9] Tits J., “Abstract and simple groups”, Ann. Math., 80:2 (1964), 313–329 | DOI | MR | Zbl

[10] Borel A., “Density and maximality of arithmetic subgroups”, J. Reine Angew. Math., 224 (1966), 78–89 | MR | Zbl

[11] Borel A., “Some finiteness properties of adele groups over number fields”, Publ. Math. IHES, 16 (1963), 101–126 | MR | Zbl

[12] Tits J., “Classification of algebraic semisimple groups”, Proc. Symp. Pure Math., v. 9, Providence, 1966, 33–63 | MR

[13] Lazard M., “Groupes analytiques $p$-adiques”, Publ. Math. IHES, 26 (1965), 5–219 | MR

[14] Shevalle K., Teoriya grupp Li, t. 2, IL, M., 1958

[15] Chevalley C., “Sur certains groupes simples”, Tohoku Math. J., 7 (1955), 14–66 | DOI | MR | Zbl

[16] Chevalley C., Seminaire sur la classification groupes de Lie algebriques, ENS, Paris, 1958

[17] Bruhat F., Tits J., “Groupes algebriques simples sur un corps local”, C. R. Acad. Sci. Paris, 263:23 (1966), 867–869 | MR | Zbl

[18] Kneser M., “Galois Kohomologie halbeinf acher algebraiscben Gruppen über $p$-adischen Körpern. I”, Math. Z., 88 (1965), 40–47 | DOI | MR | Zbl

[19] Borel A., Tits J., “Groupes reductifs”, Publ. Math. IHES, 27 (1965), 55–152 | MR

[20] Harder G., “Eine Bemerkung zum schwachen Approximationssatz”, Archiv Math., XIX:5 (1968), 465–472 | DOI | MR

[21] Dieudonne J., La geometrie des groupes classiques, Berlin, 1963 | MR

[22] Dieudonne J., Sur les groupes classiques, Paris, 1967

[23] Steinberg R., “Variations on a theme of Chevalley”, Pac. J. Math., 9 (1959), 875–891 | MR | Zbl

[24] Steinberg R., “Generateurs, relations et revetement de groupes algebriques”, Colloq. Théorie des Groupes Algébriques, Bruxelles, 1962, 113–127 | MR | Zbl

[25] Wang S., “On the commutator group of a simple algebra”, Amer. J. Math., 72:2 (1950), 323–334 | DOI | MR | Zbl

[26] Weil A., “Algebras with involutions and the classical groups”, J. Ind. Math. Soc., 24 (1961), 589–623 | MR | Zbl