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Solution of the congruence subgroup problem for \(\text{SL}_ n\) \((n\geq 3)\) and \(\text{Sp}_{2n}\) \((n\geq 2)\). (English) Zbl 0174.05203

MSC:
20H05 Unimodular groups, congruence subgroups (group-theoretic aspects)
20G15 Linear algebraic groups over arbitrary fields
Keywords:
group theory
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[1] Bass (H.), K-theory and stable algebra,Publ. I.H.E.S., no 22 (1964), 5–60. · Zbl 0248.18025
[2] –,Symplectic modules and groups (in preparation).
[3] Bass (H.), Heller (A.) andSwan (R.), The Whitehead group of a polynomial extension,Publ. I.H.E.S., no 22 (1964), 61–79. · Zbl 0248.18026
[4] Bass (H.), Lazard (M.) andSerre (J.-P.), Sous-groupes d’indice fini dans SL(n,Z),Bull. Am. Math. Soc., 385–392.
[5] Bass (H.) andMilnor (J.),Unimodular groups over number fields (mimeo. notes), Princeton University (1965).
[6] –,On the congruence subgroup problem for SL n (n) and Sp2n (n). (Notes, Inst. for Adv. Study.)
[7] Bass (H.) andMurthy (M. P.), Grothendieck groups and Picard groups of abelian group rings,Ann. of Math., 86 (1967), 16–73. · Zbl 0157.08202
[8] Borel (A.) andHarish-Chandra, Arithmetic subgroups of algebraic groups,Ann. of Math., 75 (1962), 485–535. · Zbl 0107.14804
[9] Borel (A.) andTits (J.), Groupes réductifs,Publ. I.H.E.S., no 27 (1965), 55–151.
[10] Chevalley (C.), Sur certains schémas de groupes semi-simples,Sém. Bourbaki (1961), exposé 219. · Zbl 0125.01705
[11] Higman (G.), On the units of group rings,Proc. Lond. Math. Soc., 46 (1940), 231–248. · Zbl 0025.24302
[12] Hurwitz (A.), Die unimodularen Substitutionen in einem algebraischen Zahlkörpen (1895),Mathematische Werke, vol. 2, 244–268, Basel (1933).
[13] Kneser (M.), Strong approximation, I, II, Algebraic groups and discontinuous subgroups,Proc. Symp. Pure Math., IX, A.M.S., 1966, p. 187–196.
[14] Kubota (T.), Ein arithmetischer Satz über eine Matrizengrouppe,J. reine angew. Math., 222 (1965), 55–57. · Zbl 0149.28602
[15] Matsumoto (H.), Subgroups of finite index of arithmetic groups. Algebraic groups and Discontinuous Subgroups,Proc. Symp. Pure Math., IX, A.M.S., 1966, p. 99–103.
[16] Mennicke (J.), Finite factor groups of the unimodular group,Ann. of Math., 81 (1965), 31–37. · Zbl 0135.06504
[17] —-, Zur theorie der Siegelsche Modulgruppe,Math. Ann., 159 (1965), 115–129. · Zbl 0134.26502
[18] Milnor (J.), Whitehead torsion,Bull. Am. Math. Soc., 7 (1966), 358–426. · Zbl 0147.23104
[19] Moore (C.), Extensions and low dimensional cohomology of locally compact groups, I,Trans. Am. Math. Soc., 113 (1964), 40–63. · Zbl 0131.26902
[20] O’Meara (O. T.), On the finite generation of linear groups over Hasse domains,J. reine angew. Math., 217 (1963).
[21] Raghunathan (M. S.), A vanishing theorem for the cohomology of arithmetic subgroups of algebraic groups (to appear). · Zbl 0157.06802
[22] Rege (N.), Finite generation of classical groups over Hasse domains (to appear). · Zbl 0157.06201
[23] Lazard (M.), Groupes analytiquesp-adiques,Publ. I.H.E.S., no 26 (1965), 5–219.
[24] Weil (A.), Remarks on the cohomology of groups,Ann. of Math., 80 (1964), 149–157. · Zbl 0192.12802
[25] —-, Sur certains groupes d’opérateurs unitaires,Acta Math., 111 (1964), 143–211. · Zbl 0203.03305
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