Generation of relative commutator subgroups in Chevalley groups

DOI10.1017/S0013091515000188zbMath1348.20055arXiv1212.5432OpenAlexW2963483127MaRDI QIDQ2806123

Zuhong Zhang, Nikolai A. Vavilov, Roozbeh Hazrat

Publication date: 13 May 2016

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.5432

zbMATH Keywords

generating setsChevalley groupsirreducible root systemsrelative elementary subgroupsmixed commutator subgroups

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Commutator calculus (20F12) Linear algebraic groups over adèles and other rings and schemes (20G35)

Related Items (11)

The commutators of classical groups ⋮ Commutators of elementary subgroups: curiouser and curiouser ⋮ Structure of Chevalley groups over rings via universal localization. ⋮ Commutators of congruence subgroups in the arithmetic case ⋮ Commutators of relative and unrelative elementary groups, revisited ⋮ Non-abelian \(K\)-theory for Chevalley groups over rings. ⋮ The yoga of commutators: further applications. ⋮ Unrelativized standard commutator formula ⋮ Generation of relative commutator subgroups in Chevalley groups. II ⋮ Calculations in exceptional groups, an update. ⋮ Commutators of relative and unrelative elementary unitary groups

Cites Work

• Multiple commutator formulas.
• Relative unitary commutator calculus, and applications.
• A further note on subgroups of GL(n,A) which are generated by commutators
• On subgroups of GL(n,A) which are generated by commutators
• Chevalley groups over commutative rings. I: Elementary calculations
• \(K_{1}\) of Chevalley groups are nilpotent
• The yoga of commutators: further applications.
• The yoga of commutators.
• Chevalley groups over local rings
• \(K\)-theory and stable algebra
• Bak's work on theK-theory of rings
• Relative subgroups in Chevalley groups
• On the Normal Subgroups of $G_2(A)$
• Generators, Relations and Coverings of Chevalley Groups Over Commutative Rings

This page was built for publication: Generation of relative commutator subgroups in Chevalley groups