Commutator width in Chevalley groups

Roozbeh Hazrat; Alexei Stepanov; Nikolai Vavilov; Zuhong Zhang

doi:10.1285/i15900932v33n1p139

Commutator width in Chevalley groups

Roozbeh Hazrat^*, Alexei Stepanov, Nikolai Vavilov, Zuhong Zhang

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

28 Citations (Scopus)

Abstract

The present paper is the [slightly expanded] text of our talk at the Conference " Advances in Group Theory and Applications" at Porto Cesareo in June 2011. Our main results assert that [elementary] Chevalley groups very rarely have finite commutator width. The reason is that they have very few commutators, in fact, commutators have finite width in elementary generators. We discuss also the background, bounded elementary generation, methods of proof, relative analogues of these results, some positive results, and possible generalisations.

Original language	English
Pages (from-to)	139-170
Number of pages	32
Journal	Note di Matematica
Volume	33
Issue number	1
DOIs	https://doi.org/10.1285/i15900932v33n1p139
Publication status	Published - 2013

Keywords

Bounded generation
Chevalley groups
Commutator width
Elementary generators
Elementary subgroups
Relative groups
Standard commutator formulas
Unitriangular factorisations

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10.1285/i15900932v33n1p139

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AU - Hazrat, Roozbeh

AU - Stepanov, Alexei

AU - Vavilov, Nikolai

AU - Zhang, Zuhong

PY - 2013

Y1 - 2013

N2 - The present paper is the [slightly expanded] text of our talk at the Conference " Advances in Group Theory and Applications" at Porto Cesareo in June 2011. Our main results assert that [elementary] Chevalley groups very rarely have finite commutator width. The reason is that they have very few commutators, in fact, commutators have finite width in elementary generators. We discuss also the background, bounded elementary generation, methods of proof, relative analogues of these results, some positive results, and possible generalisations.

AB - The present paper is the [slightly expanded] text of our talk at the Conference " Advances in Group Theory and Applications" at Porto Cesareo in June 2011. Our main results assert that [elementary] Chevalley groups very rarely have finite commutator width. The reason is that they have very few commutators, in fact, commutators have finite width in elementary generators. We discuss also the background, bounded elementary generation, methods of proof, relative analogues of these results, some positive results, and possible generalisations.

KW - Bounded generation

KW - Chevalley groups

KW - Commutator width

KW - Elementary generators

KW - Elementary subgroups

KW - Relative groups

KW - Standard commutator formulas

KW - Unitriangular factorisations

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SN - 1123-2536

VL - 33

SP - 139

EP - 170

JO - Note di Matematica

JF - Note di Matematica

IS - 1

ER -

Commutator width in Chevalley groups

Abstract

Keywords

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