On the congruence subgroup problem. II

DOI10.1007/BF01388793zbMath0603.20044OpenAlexW3159709446MaRDI QIDQ1082453

M. S. Raghunathan

Publication date: 1986

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143360

zbMATH Keywords

rational pointscompletionunipotent radicalsglobal fieldunipotent elementsarithmetic subgroupcongruence subgroup problemuniversal central extensionlocally compact topological groupsadèle grouparchimedean valuationsconnected simply connected absolutely simple k-algebraic groupfundamental system of neighbourhoodsk-parabolic subgroups

Mathematics Subject Classification ID

Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Semisimple Lie groups and their representations (22E46) Linear algebraic groups over global fields and their integers (20G30) Linear algebraic groups over adèles and other rings and schemes (20G35)

Related Items

VOLUME-PRESERVING ACTIONS OF SIMPLE ALGEBRAIC ℚ-GROUPS ON LOW-DIMENSIONAL MANIFOLDS ⋮ Isotropic nonarchimedean \(S\)-arithmetic groups are not left orderable. ⋮ On the congruence kernel for simple algebraic groups ⋮ An approximation principle for congruence subgroups. II: Application to the limit multiplicity problem ⋮ On the congruence subgroup problem for anisotropic groups of inner type \(A_n\) ⋮ Counting lattices in simple Lie groups: the positive characteristic case ⋮ Subgroup separability in integral group rings. ⋮ On the congruence kernel of isotropic groups over rings ⋮ Finitely generated profinitely dense free groups in higher rank semi-simple groups ⋮ Imbedding Quasi-split Groups in Isotropic Groups ⋮ Trees and discrete subgroups of Lie groups over local fields ⋮ The congruence subgroup problem. ⋮ Almost-minimal nonuniform lattices of higher rank ⋮ Centrality ⋮ Generations for arithmetic groups. ⋮ A Topological Realization of the Congruence Subgroup Kernel ⋮ On absolutely profinitely solitary lattices in higher rank Lie groups

Cites Work

• Unnamed Item
• Unnamed Item
• On the congruence subgroup problem: Determination of the Metaplectic kernel
• The congruence subgroup and metaplectic problems for \(SL_{n>1}\) of division algebras
• On the congruence subgroup problem
• Strong approximation for semi-simple groups over function fields
• Finite factor groups of the unimodular group
• Groupes reductifs
• Conjugacy classes in Lie algebras and algebraic groups
• Endliche Erzeugbarkeit arithmetischer Gruppen über Funktionenkörpern
• Solution of the congruence subgroup problem for \(\text{SL}_ n\) \((n\geq 3)\) and \(\text{Sp}_{2n}\) \((n\geq 2)\)
• Éléments unipotents et sous-groupes paraboliques de groupes réductifs. I
• Le problème des groupes de congruence pour \(SL_2\)
• Minkowskische Reduktionstheorie über Funktionenkörpern
• On Central Extensions of Rational Points of Algebraic Groups
• Normalteiler ganzzahliger Spingruppen.
• THE PROBLEM OF STRONG APPROXIMATION AND THE KNESER-TITS CONJECTURE FOR ALGEBRAIC GROUPS
• Sous-groupes d'indice fini dans $SL\left( {n,Z} \right)$
• Sur les sous-groupes arithmétiques des groupes semi-simples déployés