Finiteness properties of solvable S-arithmetic groups: An example

DOI10.1016/0022-4049(87)90016-8zbMath0617.20020OpenAlexW1991439388MaRDI QIDQ1821869

K. Stephen Brown, Herbert Abels

Publication date: 1987

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(87)90016-8

zbMATH Keywords

simplicial complexisotropy groupBruhat-Tits buildingprojective resolutionfinite presentationtype \(FP_ n\)S-arithmetic groups over number fieldssimplicial actionsolvable algebraic matrix group

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Generators, relations, and presentations of groups (20F05) Homological methods in group theory (20J05) Linear algebraic groups over global fields and their integers (20G30) Cohomology theory for linear algebraic groups (20G10) Abstract complexes in algebraic topology (55U05)

Related Items (13)

Homologically trivial actions on chain complexes and finiteness properties of infinite groups ⋮ Finiteness properties of soluble arithmetic groups over global function fields. ⋮ On the Finiteness length of some soluble linear groups ⋮ Word problems and a homological finiteness condition for monoids ⋮ Infinite presentability of groups and condensation ⋮ Abels's groups revisited. ⋮ Brown's criterion and classifying spaces for families ⋮ The Σ-invariants of 𝑆-arithmetic subgroups of Borel groups ⋮ Presentability by products for some classes of groups ⋮ Simple groups separated by finiteness properties ⋮ Finiteness properties of certain arithmetic groups in the function field case ⋮ Finiteness properties of groups ⋮ Amenable groups without finitely presented amenable covers

Cites Work

• A connection between the integral homology and the centre of a rational linear group
• Homological properties of certain arithmetic groups in the function field case
• Cohomologie d'immeubles et de groupes S-arithmétiques
• Bieri-Strebel Valuations (of Finite Rank)
• A Finitely Presented Group Whose 3-Dimensional Integral Homology is not Finitely Generated
• Finiteness properties of groups
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