The congruence subgroup and metaplectic problems for \(SL_{n>1}\) of division algebras

DOI10.1016/0021-8693(82)90094-1zbMath0495.20022OpenAlexW2053944379MaRDI QIDQ1169562

Anthony Bak, Ulf Rehmann

Publication date: 1982

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(82)90094-1

zbMATH Keywords

group of rational pointscongruence kernelcongruence subgroupsalmost simple algebraic groupfinite central division algebra

Mathematics Subject Classification ID

Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Linear algebraic groups over global fields and their integers (20G30)

Related Items

Lower bounds for \(K_ 2^{top}({\hat {\mathbb{Z}}}_ p\pi)\) and \(K_ 2({\mathbb{Z}}\pi)\), On the congruence subgroup problem. II, Bak's work on theK-theory of rings, Computation of the metaplectic kernel, Linear groups over general rings. I: Generalities., Abelianization and fixed point properties of units in integral group rings, Linear groups, The congruence subgroup problem., From the Poincaré Theorem to generators of the unit group of integral group rings of finite groups, Units of group rings, \(K_ 2\) of p-adic group rings of abelian p-groups, UNITARY UNITS IN INTEGRAL GROUP RINGS, On the congruence subgroup problem: Determination of the Metaplectic kernel, Generators of large subgroups of the unit group of integral group rings

Cites Work

• \(SK_1\) von Schiefkörpern. Seminar Bielefeld-Göttingen, 1976
• On a functional property of power residue symbols
• \(K_2\) of discrete valuation rings
• Odd dimension surgery groups of odd torsion groups vanish
• On the congruence subgroup problem
• \(K_2\) of quaternion algebras
• Group extensions of p-adic and adelic linear groups
• Solution of the congruence subgroup problem for \(\text{SL}_ n\) \((n\geq 3)\) and \(\text{Sp}_{2n}\) \((n\geq 2)\)
• Le problème des groupes de congruence pour \(SL_2\)
• Moore's theorem on uniqueness of reciprocity laws
• On Grunwald's theorem
• SK ₁ for Finite Group Rings: IV
• THE STRUCTURE OF CLASSICAL ARITHMETIC GROUPS OF RANK GREATER THAN ONE
• Zentrale Erweiterungen der speziellen linearen Gruppe eines Schiefkörpers.
• Starke Approximation in algebraischen Gruppen. I.
• Introduction to Algebraic K-Theory. (AM-72)
• Sur les sous-groupes arithmétiques des groupes semi-simples déployés
• Surjective Stability in Dimension 0 for K 2 and Related Functors
• On the Commutator Group of a Simple Algebra
• Über die multiplikative Gruppe einer $\mathfrak{p}$-adischen Divisionsalgebra
• On \(K_2\) of finite dimensional division algebras over arithmetical fields
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