Quantifying residual finiteness of arithmetic groups

DOI10.1112/S0010437X11007469zbMath1256.20030arXiv1008.3579MaRDI QIDQ2894208

Khalid Bou-Rabee, Tasho Kaletha

Publication date: 29 June 2012

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.3579

zbMATH Keywords

subgroups of finite indexfinitely generated residually finite groupsgrowth functionsarithmetic groupsresidual finitenessnormal residual finiteness growth

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Discrete subgroups of Lie groups (22E40) Structure of modular groups and generalizations; arithmetic groups (11F06) Asymptotic properties of groups (20F69) Residual properties and generalizations; residually finite groups (20E26)

Related Items (14)

Zariski closures and subgroup separability ⋮ Full residual finiteness growths of nilpotent groups ⋮ Groups with near exponential residual finiteness growth ⋮ Residual dimension of nilpotent groups ⋮ Intersection growth in groups ⋮ The primitivity index function for a free group, and untangling closed curves on hyperbolic surfaces.With the appendix by Khalid Bou–Rabee ⋮ Expected depth of random walks on groups ⋮ Quantifying residual finiteness of linear groups ⋮ Systolic growth of linear groups ⋮ Residual finiteness growths of virtually special groups. ⋮ Local commensurability graphs of solvable groups ⋮ Effective twisted conjugacy separability of nilpotent groups ⋮ Extremal behavior of divisibility functions. ⋮ Primitivity index bounds in free groups, and the second Chebyshev function

Cites Work

• Die adjungierten Darstellungen der Chevalley-Gruppen
• Unrefined minimal \(K\)-types for \(p\)-adic groups
• Quantifying residual finiteness.
• Bounding the residual finiteness of free groups
• The word and Riemannian metrics on lattices of semisimple groups

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