On the word length of commutators in \(\text{GL}_n(R)\)

DOI10.1023/A:1007730801851zbMath0935.20037MaRDI QIDQ1306921

Alexei Stepanov, Alexander S. Sivatski

Publication date: 5 December 1999

Published in: \(K\)-Theory (Search for Journal in Brave)

zbMATH Keywords

general linear groupselementary subgroupsstable rangeword lengthsSteinberg groupsdimensions of maximal spectra of ringsproducts of elementary transvections

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) Stable range conditions (19B10)

Related Items

Bounded reduction of orthogonal matrices over polynomial rings, The commutators of classical groups, Linear groups over general rings. I: Generalities., 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., Calculations in exceptional groups over rings., Relative unitary commutator calculus, and applications., The width of the group \(\mathrm{GL}(6,K)\) with respect to a set of quasiroot elements., Non-abelian \(K\)-theory for Chevalley groups over rings., Decomposition of unipotents for \(\mathrm{E}_6\) and \(\mathrm{E}_7\): 25 years after, Unitriangular factorizations of Chevalley groups., On the length of commutators in Chevalley groups., The yoga of commutators., Unnamed Item, Chevalley groups of type E7 in the 56-dimensional representation, Ranks of subgroups in boundedly generated groups, Width of groups of type $\mathrm E_{6}$ with respect to root elements. I, Commutators of relative and unrelative elementary unitary groups, \(K_{1}\) of Chevalley groups are nilpotent