On the Finiteness length of some soluble linear groups

DOI10.4153/S0008414X21000213MaRDI QIDQ5046558

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Publication date: 8 November 2022

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.06704

zbMATH Keywords

finiteness properties\(S\)-arithmetic groupsabels' groupssoluble group schemes

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Topological methods in group theory (57M07) Linear algebraic groups over global fields and their integers (20G30) Other matrix groups over rings (20H25)

Related Items

The Σ-invariants of 𝑆-arithmetic subgroups of Borel groups, Higher generating subgroups and Cohen–Macaulay complexes

Cites Work

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• The braided Thompson's groups are of type \(F_\infty\)
• Abels's groups revisited.
• Filling boundaries of coarse manifolds in semisimple and solvable arithmetic groups
• On groups with quasidiagonal \(C^\ast\)-algebras
• Higher finiteness properties of braided groups
• Presentations for groups acting on simply-connected complexes
• On the isolated points in the space of groups.
• Finiteness properties of arithmetic groups over function fields.
• \(\text{SL}_n(\mathbb{Z}[t)\) is not \(\text{FP}_{n-1}\).]
• A family of solvable linear groups that do not satisfy the maximal condition on normal subgroups
• Finite presentability of S-arithmetic groups. Compact presentability of solvable groups
• A connection between the integral homology and the centre of a rational linear group
• Buildings of spherical type and finite BN-pairs
• Cohomologie d'immeubles et de groupes S-arithmétiques
• Finiteness conditions on groups and quasi-isometries
• A local-global principle for finiteness properties of \(S\)-arithmetic groups over number fields
• Higher generation subgroup sets and the \(\Sigma\)-invariants of graph groups
• Simple groups separated by finiteness properties
• The \(FP_ m\)-conjecture for a class of metabelian groups
• Chevalley groups over commutative rings. I: Elementary calculations
• Finiteness properties of solvable S-arithmetic groups: An example
• Finiteness conditions for groups
• Contraction groups and scales of automorphisms of totally disconnected locally compact groups
• Finiteness properties of soluble arithmetic groups over global function fields.
• Higher finiteness properties of reductive arithmetic groups in positive characteristic: the rank theorem.
• Stability and invariant random subgroups
• Reductive groups over a local field
• On the finite presentation of subdirect products and the nature of residually free groups
• Infinite presentability of groups and condensation
• Lectures on Chevalley Groups
• Bounding the homological finiteness length
• On Simple Groups of Type B n
• On Automorphisms of Lie Algebras of Classical Type. II
• Buildings
• Valuations and Finitely Presented Metabelian Groups
• Arithmetic groups over function fields I
• Homological finiteness conditions for a class of metabelian groups
• The K(π, 1)-Problem for Hyperplane Complements Associated to Infinite Reflection Groups
• Amenable groups without finitely presented amenable covers
• Higher generating subgroups and Cohen–Macaulay complexes
• Construction of Certain Semi-Simple Groups^*
• On the finite generation of linear groups over Hasse domains.
• Dehn function and asymptotic cones of Abels’ group
• On the simple connectedness of certain subsets of buildings
• Higher generation by subgroups
• Finiteness properties of groups