Bass, H.; Milnor, John W.; Serre, Jean-Pierre Solution of the congruence subgroup problem for \(\text{SL}_ n\) \((n\geq 3)\) and \(\text{Sp}_{2n}\) \((n\geq 2)\). (English) Zbl 0174.05203 Publ. Math., Inst. Hautes Étud. Sci. 33, 59-137 (1967). Reviewer: J. Dieudonné Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 13 ReviewsCited in 235 Documents MSC: 20H05 Unimodular groups, congruence subgroups (group-theoretic aspects) 20G15 Linear algebraic groups over arbitrary fields Keywords:group theory × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML References: [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 · doi:10.2307/1970360 [8] Borel (A.) andHarish-Chandra, Arithmetic subgroups of algebraic groups,Ann. of Math., 75 (1962), 485–535. · Zbl 0107.14804 · doi:10.2307/1970210 [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 · doi:10.1112/plms/s2-46.1.231 [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 · doi:10.2307/1970380 [17] —-, Zur theorie der Siegelsche Modulgruppe,Math. Ann., 159 (1965), 115–129. · Zbl 0134.26502 · doi:10.1007/BF01360285 [18] Milnor (J.), Whitehead torsion,Bull. Am. Math. Soc., 7 (1966), 358–426. · Zbl 0147.23104 · doi:10.1090/S0002-9904-1966-11484-2 [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 · doi:10.2307/1970495 [25] —-, Sur certains groupes d’opérateurs unitaires,Acta Math., 111 (1964), 143–211. · Zbl 0203.03305 · doi:10.1007/BF02391012 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.