Normality of the elementary subgroups of twisted Chevalley groups over commutative rings

DOI10.1006/jabr.1995.1199zbMath0840.20043OpenAlexW1984811046MaRDI QIDQ1895635

Kazuo Suzuki

Publication date: 29 August 1995

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1995.1199

zbMATH Keywords

normal subgroupsgroup of unitsmaximal idealscommutative ringstwisted Chevalley groupssubgroup generated by root elements

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Linear algebraic groups over adèles and other rings and schemes (20G35)

Related Items (16)

An $\mathrm {A}_2$-proof of structure theorems for Chevalley groups of types $\mathrm {E}_6$ and $\mathrm {E}_7$ ⋮ The commutators of classical groups ⋮ Relative commutator calculus in Chevalley groups. ⋮ AN A₃-PROOF OF STRUCTURE THEOREMS FOR CHEVALLEY GROUPS OF TYPES E₆ AND E₇ ⋮ Calculations in exceptional groups over rings. ⋮ Odd unitary groups. ⋮ The yoga of commutators: further applications. ⋮ Relative subgroups in Chevalley groups ⋮ Chevalley groups of type E7 in the 56-dimensional representation ⋮ Localization-completion strikes again: relative \(K_1\) is nilpotent by Abelian ⋮ $\mathrm A_2$-proof of structure theorems for Chevalley groups of type $\mathrm F_4$ ⋮ Elementary subgroups of isotropic reductive groups ⋮ Normality of DSER elementary orthogonal group ⋮ Basic reductions in the description of normal subgroups. ⋮ Another presentation for symplectic Steinberg groups ⋮ \(K_{1}\) of Chevalley groups are nilpotent

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