Commensurated subgroups of arithmetic groups, totally disconnected groups and adelic rigidity

DOI10.1007/s00039-013-0236-5zbMath1295.22017arXiv0911.1966OpenAlexW1973909385MaRDI QIDQ382292

George A. Willis, Yehuda Shalom

Publication date: 18 November 2013

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.1966

zbMATH Keywords

commensurated subgroup problemMargulis-Zimmer conjectureouter commensurate normalizer propertystandard commensurated subgroup

Mathematics Subject Classification ID

Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) General structure theorems for groups (20E34) Discrete subgroups of Lie groups (22E40) Linear algebraic groups over global fields and their integers (20G30)

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Cites Work

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• The Margulis-Platonov conjecture for \(\text{SL}_{1,D}\) and 2-generation of finite simple groups.
• The direction of an automorphism of a totally disconnected locally compact group
• Bounded generation of \(S\)-arithmetic subgroups of isotropic orthogonal groups over number fields.
• Weakly commensurable arithmetic groups and isospectral locally symmetric spaces
• Torsion in cocompact lattices in coverings of Spin(2,n)
• On the congruence subgroup problem: Determination of the Metaplectic kernel
• Strong approximation for Zariski-dense subgroups of semi-simple algebraic groups
• Finite presentability of S-arithmetic groups. Compact presentability of solvable groups
• Subgroups close to normal subgroups
• Operationen mit periodischen Stabilisatoren
• Real vector bundles with discrete structure group
• Concentration functions and a class of non-compact groups
• On the congruence subgroup problem
• Scale functions on linear groups over local skew fields
• Scale functions on \(p\)-adic Lie groups
• Projective varieties with non-residually finite fundamental group
• The structure of totally disconnected, locally compact groups
• Central extensions of simply connected algebraic groups and Galois cohomology
• Computation of the metaplectic kernel
• Tidy subgroups for commuting automorphisms of totally disconnected groups: An analogue of simultaneous triangularisation of matrices
• Deligne's topological central extension is universal.
• Rigidity of commensurators and irreducible lattices
• The congruence subgroup problem.
• Zariski dense subgroups of arithmetic groups
• Subgroup growth.
• Contraction groups and scales of automorphisms of totally disconnected locally compact groups
• Concentration functions in locally compact groups
• Representation growth of linear groups
• Bounded generation of \(\text{SL}(n,A)\) (after D. Carter, G. Keller, and E. Paige).
• Finite factor groups of the unimodular group
• Group extensions of p-adic and adelic linear groups
• Solution of the congruence subgroup problem for \(\text{SL}_ n\) \((n\geq 3)\) and \(\text{Sp}_{2n}\) \((n\geq 2)\)
• Sur certains groupes d'opérateurs unitaires
• On some Bruhat decomposition and the structure of the Hecke rings of \(p\)-adic Chevalley groups
• Le problème des groupes de congruence pour \(SL_2\)
• Moyennes invariantes et représentations unitaires
• Bounded Elementary Generation of SL n (O)
• Structure Theory of Totally Disconnected Locally Compact Groups via Graphs and Permutations
• Compact Extensions of Compactly Generated Nilpotent Groups are Pro-Lie
• Compactness Properties of Topological Groups. III
• Normalteiler ganzzahliger Spingruppen.
• Almost Invariant Families
• Sous-groupes d'indice fini dans $SL\left( {n,Z} \right)$
• Sur les sous-groupes arithmétiques des groupes semi-simples déployés
• Bounded generation and Kazhdan's property (T)
• Further properties of the scale function on a totally disconnected group
• The word and Riemannian metrics on lattices of semisimple groups
• Arithmetic structure of fundamental groups and actions of semisimple Lie groups