On the length of commutators in Chevalley groups.

DOI10.1007/s11856-011-0109-2zbMath1262.20054OpenAlexW2069611666MaRDI QIDQ1758932

Alexei Stepanov, Nikolai A. Vavilov

Publication date: 19 November 2012

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

Full work available at URL: https://doi.org/10.1007/s11856-011-0109-2

zbMATH Keywords

widthsroot systemsunipotent elementsproducts of commutatorssimply connected Chevalley groups

Mathematics Subject Classification ID

Commutator calculus (20F12) Linear algebraic groups over adèles and other rings and schemes (20G35) Stability for linear groups (19B14)

Related Items (21)

Bounded reduction of orthogonal matrices over polynomial rings ⋮ The commutators of classical groups ⋮ \(\mathrm{SL}_2\)-factorizations of Chevalley groups. ⋮ Involution widths of skew linear groups generated by involutions ⋮ Bounded reduction for Chevalley groups of types \(E_6\) and \(E_7\) ⋮ Bounded generation and commutator width of Chevalley groups: function case ⋮ Commutators of elementary subgroups: curiouser and curiouser ⋮ Structure of Chevalley groups over rings via universal localization. ⋮ Relative commutator calculus in Chevalley groups. ⋮ Calculations in exceptional groups over rings. ⋮ Relative unitary commutator calculus, and applications. ⋮ Non-abelian \(K\)-theory for Chevalley groups over rings. ⋮ Decomposition of unipotents for \(\mathrm{E}_6\) and \(\mathrm{E}_7\): 25 years after ⋮ Local-global principle for congruence subgroups of Chevalley groups. ⋮ Unitriangular factorizations of Chevalley groups. ⋮ The yoga of commutators. ⋮ Chevalley groups of type E7 in the 56-dimensional representation ⋮ Generation of relative commutator subgroups in Chevalley groups. II ⋮ Calculations in exceptional groups, an update. ⋮ Commutators of relative and unrelative elementary unitary groups ⋮ Multiple commutator formulas for unitary groups

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