Standard commutator formula, revisited.
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Publication:1759460
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
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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