Standard commutator formula, revisited.

DOI10.3103/S1063454110010036zbMath1254.20038OpenAlexW2014218700MaRDI QIDQ1759460

Alexei Stepanov, Nikolai A. Vavilov

Publication date: 21 November 2012

Published in: Vestnik St. Petersburg University. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s1063454110010036

zbMATH Keywords

elementary subgroupsprincipal congruence subgroupscommutator formulaelinear groups over rings

Mathematics Subject Classification ID

Other matrix groups over rings (20H25) Commutator calculus (20F12) Linear algebraic groups over adèles and other rings and schemes (20G35)

Related Items (18)

Relative centralizers of relative subgroups ⋮ The commutators of classical groups ⋮ Multiple commutator formulas. ⋮ Multiple commutators of elementary subgroups: end of the line ⋮ Commutators of elementary subgroups: curiouser and curiouser ⋮ Structure of Chevalley groups over rings via universal localization. ⋮ Commutators of congruence subgroups in the arithmetic case ⋮ Relative commutator calculus in Chevalley groups. ⋮ Commutators of relative and unrelative elementary groups, revisited ⋮ Toward the reverse decomposition of unipotents. II: The relative case ⋮ Relative unitary commutator calculus, and applications. ⋮ Non-abelian \(K\)-theory for Chevalley groups over rings. ⋮ Local-global principle for congruence subgroups of Chevalley groups. ⋮ The yoga of commutators. ⋮ Unrelativized standard commutator formula ⋮ Generation of relative commutator subgroups in Chevalley groups. II ⋮ Commutators of relative and unrelative elementary unitary groups ⋮ Multiple commutator formulas for unitary groups

Cites Work

• Linear groups over general rings. I: Generalities.
• Standard commutator formula.
• Localization-completion strikes again: relative \(K_1\) is nilpotent by Abelian
• A module structure on certain orbit sets of unimodular rows
• A further note on subgroups of GL(n,A) which are generated by commutators
• Nonabelian \(K\)-theory: The nilpotent class of \(K_ 1\) and general stability
• On the normal structure of the general linear group over a ring
• On subgroups of GL(n,A) which are generated by commutators
• Dimension theory and nonstable \(K_{1}\) of quadratic modules
• \(K_{1}\) of Chevalley groups are nilpotent
• Relativizing functors on rings and algebraic K-theory
• Elementary subgroups of isotropic reductive groups
• Bak's work on theK-theory of rings
• THE GROUP OF UNITS OF A FREE PRODUCT OF RINGS
• Structure of Hyperbolic Unitary Groups I: Elementary Subgroups
• Overgroups of elementary symplectic groups
• ON THE STABILIZATION OF THE GENERAL LINEAR GROUP OVER A RING

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