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The commutators of classical groups (Q2397380)

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Language	Label	Description	Also known as
English	The commutators of classical groups	scientific article

Statements

scholarly article

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The commutators of classical groups (English)

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Nikolai A. Vavilov

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Journal of Mathematical Sciences (New York)

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publication date

22 May 2017

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full work available at URL

https://arxiv.org/abs/1510.07143

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MaRDI profile type

MaRDI publication profile

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Whitehead groups of chevalley groups over polynomial rings

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Writing certain commutators as products of cubes in free groups

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Writing Commutators of Commutators as Products of Cubes in Groups

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Local-global principle for congruence subgroups of Chevalley groups.

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K-Theory of Forms. (AM-98)

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Nonabelian \(K\)-theory: The nilpotent class of \(K_ 1\) and general stability

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Local-global principle for transvection groups

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Localization-completion strikes again: relative \(K_1\) is nilpotent by Abelian

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Dimension theory and nonstable K-theory for net groups

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Normality for elementary subgroup functors

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Structure of Hyperbolic Unitary Groups I: Elementary Subgroups

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\(K\)-theory and stable algebra

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Solution of the congruence subgroup problem for \(\text{SL}_ n\) \((n\geq 3)\) and \(\text{Sp}_{2n}\) \((n\geq 2)\)

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Excision in algebraic \(K\)-theory

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Schur multiplier of a group of elementary matrices of finite order

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Location of subgroups in the general linear group over a commutative ring

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Non-abelian \(K\)-theory for Chevalley groups over rings.

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On a question of M. Newman on the number of commutators

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Commutators in linear groups

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On the conjectures of J. Thompson and O. Ore

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Stable range in commutative rings

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K 2 Measures Excision for K 1

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Subgroups of the elementary and Steinberg groups of congruence level \(I^ 2\)

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Products of conjugacy classes and fixed point spaces

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A classification of subgroups of \(\Lambda\)-quadratic groups normalized by relative elementary groups

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Dimension theory and nonstable \(K_{1}\) of quadratic modules

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Relative subgroups in Chevalley groups

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The yoga of commutators.

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Commutator width in Chevalley groups

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\(K_{1}\) of Chevalley groups are nilpotent

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Bak's work on the<i>K</i>-theory of rings

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Relative unitary commutator calculus, and applications.

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Relative commutator calculus in Chevalley groups.

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Multiple commutator formulas for unitary groups

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Generation of relative commutator subgroups in Chevalley groups

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Multiple commutator formulas.

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Basic Commutators in Weights Six and Seven as Relators

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Basic commutators as relators

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A module structure on certain orbit sets of unimodular rows

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Absolute stable rank and Witt cancellation for noncommutative rings

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THE STABILIZATION OF SYMPLECTIC GROUPS OVER A POLYNOMIAL RING

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Quillen-Suslin theory for a structure theorem for the Elementary Symplectic Group

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The structure of orthogonal groups over arbitrary commutative rings

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Word maps and Waring type problems

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The Waring problem for finite simple groups.

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Unitary Steinberg group is centrally closed

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The structure of symplectic groups over arbitrary commutative rings

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A generalized sandwich theorem

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The Ore conjecture.

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Commutators in finite quasisimple groups

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Elementary subgroup of an isotropic reductive group is perfect

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A Note on Subgroups of GL(<i>n, A</i> ) which are Generated by Commutators

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On subgroups of GL (n, A) which are generated by commutators. II.

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A further note on subgroups of GL(n,A) which are generated by commutators

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On subgroups of GL(n,A) which are generated by commutators

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Sur les sous-groupes arithmétiques des groupes semi-simples déployés

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Algebraic \(K\)-theory and quadratic forms. With an appendix by J. Tate

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Introduction to Algebraic K-Theory. (AM-72)

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Group extensions of p-adic and adelic linear groups

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Bounded generation of \(\text{SL}(n,A)\) (after D. Carter, G. Keller, and E. Paige).

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Overgroups of unitary groups.

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Odd unitary groups.

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<sup>1</sup>-Homotopy of Chevalley Groups

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Elementary subgroups of isotropic reductive groups

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Projective modules over polynomial rings

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Higher algebraic K-theory: I

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The higher lower central series

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

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Word maps, conjugacy classes, and a noncommutative Waring-type theorem.

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Gauss decomposition for Chevalley groups, revisited

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Homotopy invariance of non-stable <i>K</i><sub>1</sub>-functors

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Generators, Relations and Coverings of Chevalley Groups Over Commutative Rings

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Structure of Chevalley groups over rings via universal localization.

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Decomposition of transvections: A theme with variations

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On the length of commutators in Chevalley groups.

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Subgroups of classical groups normalized by relative elementary groups.

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Quadratic modules and the orthogonal group over polynomial rings

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

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Hermitian groups and \(K\)-theory

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THE STEINBERG GROUP OF A POLYNOMIAL RING

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The subnormal structure of general linear groups

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On normal subgroups of Chevalley groups over commutative rings

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Normal Subgroups of Orthogonal Groups Over Commutative Rings

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Normal subgroups of symplectic groups over rings

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The subnormal structure of general linear groups over rings

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SERRE'S PROBLEM ON PROJECTIVE MODULES OVER POLYNOMIAL RINGS, AND ALGEBRAIC $ K$-THEORY

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Normal subgroups of classical groups over rings

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A note on the subnormal structure of general linear groups

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A third look at weight diagrams

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Calculations in exceptional groups over rings.

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Overgroups of elementary symplectic groups

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Chevalley groups over commutative rings. I: Elementary calculations

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Standard commutator formula.

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Standard commutator formula, revisited.

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Linear groups over general rings. I: Generalities.

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Polynomial extensions and excision for \(K_1\)

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On homotopy invariance for homology of rank two groups.

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Stable sandwich classification theorem for classical-like groups

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Subnormal structure of non-stable unitary groups over rings.

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On the Normal Subgroups of $G_2(A)$

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.1007/S10958-017-3318-3

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Sitelinks

Mathematics(1 entry)

mardi Publication:2397380

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