Standard commutator formula.

DOI10.3103/S1063454108010020zbMath1147.20042OpenAlexW2047708208MaRDI QIDQ946037

Alexei Stepanov, Nikolai A. Vavilov

Publication date: 22 September 2008

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

Full work available at URL: https://doi.org/10.3103/s1063454108010020

zbMATH Keywords

elementary subgroupsprincipal congruence subgroupsdecompositions of unipotentscommutator formulae

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

Decomposition of transvections for automorphisms. ⋮ Relative centralizers of relative subgroups ⋮ The commutators of classical groups ⋮ Linear groups over general rings. I: Generalities. ⋮ 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. ⋮ Standard commutator formula, revisited. ⋮ The yoga of commutators. ⋮ More variations on the decomposition of transvections. ⋮ Unrelativized standard commutator formula ⋮ Chevalley groups of type E7 in the 56-dimensional representation ⋮ Localization-completion strikes again: relative \(K_1\) is nilpotent by Abelian ⋮ Basic reductions in the description of normal subgroups. ⋮ Commutators of relative and unrelative elementary unitary groups ⋮ Multiple commutator formulas for unitary groups

Cites Work

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• On subgroups of GL(n,A) which are generated by commutators
• \(K_{1}\) of Chevalley groups are nilpotent
• Decomposition of transvections: A theme with variations
• \(K\)-theory and stable algebra
• On subgroups of GL (n, A) which are generated by commutators. II.
• Structure of Hyperbolic Unitary Groups I: Elementary Subgroups

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