Relative subgroups in Chevalley groups

DOI10.1017/is010003002jkt111zbMath1204.20066OpenAlexW2113398815MaRDI QIDQ3580645

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Publication date: 13 August 2010

Published in: Journal of K-theory (Search for Journal in Brave)

Full work available at URL: https://pure.qub.ac.uk/ws/files/674429/HazratPetrovVavilov.pdf

zbMATH Keywords

elementary subgroupsChevalley groupscongruence subgroups

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Subgroup theorems; subgroup growth (20E07) Linear algebraic groups over adèles and other rings and schemes (20G35)

Related Items (15)

The commutators of classical groups ⋮ Linear groups over general rings. I: Generalities. ⋮ On subgroups normalized by \(\mathrm{EO}(2l,R)\). ⋮ Relative commutator calculus in Chevalley groups. ⋮ Calculations in exceptional groups over rings. ⋮ Chevalley groups of type \(E_7\) in the 56-dimensional representation. ⋮ Relative unitary commutator calculus, and applications. ⋮ The yoga of commutators: further applications. ⋮ The yoga of commutators. ⋮ Towards the reverse decomposition of unipotents ⋮ Chevalley groups of type E7 in the 56-dimensional representation ⋮ Generation of relative commutator subgroups in Chevalley groups ⋮ Generation of relative commutator subgroups in Chevalley groups. II ⋮ $\mathrm A_2$-proof of structure theorems for Chevalley groups of type $\mathrm F_4$ ⋮ Calculations in exceptional groups, an update.

Cites Work

• Unnamed Item
• Unnamed Item
• Odd unitary groups.
• Localization-completion strikes again: relative \(K_1\) is nilpotent by Abelian
• Net subgroups of Chevalley groups
• Quadratic modules and the orthogonal group over polynomial rings
• On the normal structure of the general linear group over a ring
• Overgroups of unitary groups.
• Dimension theory and nonstable \(K_{1}\) of quadratic modules
• Chevalley groups over commutative rings. I: Elementary calculations
• \(K_{1}\) of Chevalley groups are nilpotent
• Normality of the elementary subgroups of twisted Chevalley groups over commutative rings
• Decomposition of transvections: A theme with variations
• Chevalley groups over local rings
• Relativizing functors on rings and algebraic K-theory
• THE STABILIZATION OF SYMPLECTIC GROUPS OVER A POLYNOMIAL RING
• Factorizability of matrix functions: A direct proof
• Weight elements of Chevalley groups
• Bak's work on theK-theory of rings
• The structure of symplectic groups over arbitrary commutative rings
• On the Normal Subgroups of $G_2(A)$
• Structure of Hyperbolic Unitary Groups I: Elementary Subgroups
• Normality for elementary subgroup functors
• An $\mathrm {A}_2$-proof of structure theorems for Chevalley groups of types $\mathrm {E}_6$ and $\mathrm {E}_7$
• AN A₃-PROOF OF STRUCTURE THEOREMS FOR CHEVALLEY GROUPS OF TYPES E₆ AND E₇
• Ideals in Chevalley Algebras
• Chevalley groups over commutative rings
• Some Normal Subgroups of Elementary Subgroups of Chevalley Groups Over Rings
• Generators, Relations and Coverings of Chevalley Groups Over Commutative Rings
• On normal subgroups of Chevalley groups over commutative rings
• On normal subgroups of Chevalley groups over commutative rings

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