Finiteness properties of Chevalley groups over \(\mathbb{F}_ q[t]\)

DOI10.1007/BF02772995zbMath0809.20034MaRDI QIDQ1335158

Peter Abramenko

Publication date: 27 September 1994

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

zbMATH Keywords

arithmetic groupsBruhat-Tits buildingprojective resolutionfinite presentationEilenberg-MacLane complexfinite set of generatorstype \(FP_ n\)simple Chevalley groupfiniteness lengthfinite \(n\)-skeletonfinitely generated \(\mathbb{Z}\Gamma\)- modulestype \(F_ n\)

Mathematics Subject Classification ID

Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Generators, relations, and presentations of groups (20F05) Homological methods in group theory (20J05) Discrete subgroups of Lie groups (22E40) Linear algebraic groups over global fields and their integers (20G30) Discontinuous groups of transformations (57S30) Groups with a (BN)-pair; buildings (20E42)

Related Items

Linear groups over general rings. I: Generalities. ⋮ Finiteness properties of arithmetic groups over function fields. ⋮ Quasi-isometric rigidity of higher rank \(S\)-arithmetic lattices. ⋮ Cohomological finiteness conditions for elementary amenable groups ⋮ An infinitely generated virtual cohomology group for noncocompact arithmetic groups over function fields.

Cites Work

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• Cohomologie d'immeubles et de groupes S-arithmétiques
• Homotopy properties of the poset of nontrivial p-subgroups of a group
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• Higher generation by subgroups
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