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Bounded generation and commutator width of Chevalley groups: function case. / Kunyavski, Boris; Plotkin, Eugene; Vavilov, Nikolai .

In: European Journal of Mathematics, Vol. 9, 53, 18.05.2022.

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

Harvard

Kunyavski, B, Plotkin, E & Vavilov, N 2022, 'Bounded generation and commutator width of Chevalley groups: function case', European Journal of Mathematics, vol. 9, 53. https://doi.org/10.48550/arXiv.2204.10951, https://doi.org/10.1007/s40879-023-00627-y

APA

Kunyavski, B., Plotkin, E., & Vavilov, N. (2022). Bounded generation and commutator width of Chevalley groups: function case. Manuscript submitted for publication. https://doi.org/10.48550/arXiv.2204.10951, https://doi.org/10.1007/s40879-023-00627-y

Vancouver

Kunyavski B, Plotkin E, Vavilov N. Bounded generation and commutator width of Chevalley groups: function case. European Journal of Mathematics. 2022 May 18;9. 53. https://doi.org/10.48550/arXiv.2204.10951, https://doi.org/10.1007/s40879-023-00627-y

Author

Kunyavski, Boris ; Plotkin, Eugene ; Vavilov, Nikolai . / Bounded generation and commutator width of Chevalley groups: function case. In: European Journal of Mathematics. 2022 ; Vol. 9.

BibTeX

@article{f7fe802047e94287a58b47a3dfdb1d69,
title = "Bounded generation and commutator width of Chevalley groups: function case",
abstract = "We prove that Chevalley groups over polynomial rings $\mathbb F_q[t]$ and over Laurent polynomial $\mathbb F_q[t,t^{-1}]$ rings, where $\mathbb F_q$ is a finite field, are boundedly elementarily generated. Using this we produce explicit bounds of the commutator width of these groups. Under some additional assumptions, we prove similar results for other classes of Chevalley groups over Dedekind rings of arithmetic rings in positive characteristic. As a corollary, we produce explicit estimates for the commutator width of affine Kac--Moody groups defined over finite fields. The paper contains also a broader discussion of the bounded generation problem for groups of Lie type, some applications and a list of unsolved problems in the field.",
keywords = "Chevalley groups, elementary generators, commutators, bounded generation, Dedekind rings of arithmetic type, Chevalley groups, Kac–Moody groups, bounded generation, Polynomial rings, First order rigidity",
author = "Boris Kunyavski and Eugene Plotkin and Nikolai Vavilov",
note = "Kunyavskiĭ, B., Plotkin, E. & Vavilov, N. Bounded generation and commutator width of Chevalley groups: function case. European Journal of Mathematics 9, 53 (2023). https://doi.org/10.1007/s40879-023-00627-y",
year = "2022",
month = may,
day = "18",
doi = "10.48550/arXiv.2204.10951",
language = "English",
volume = "9",
journal = "European Journal of Mathematics",
issn = "2199-675X",
publisher = "Springer Nature",

}

RIS

TY - JOUR

T1 - Bounded generation and commutator width of Chevalley groups: function case

AU - Kunyavski, Boris

AU - Plotkin, Eugene

AU - Vavilov, Nikolai

N1 - Kunyavskiĭ, B., Plotkin, E. & Vavilov, N. Bounded generation and commutator width of Chevalley groups: function case. European Journal of Mathematics 9, 53 (2023). https://doi.org/10.1007/s40879-023-00627-y

PY - 2022/5/18

Y1 - 2022/5/18

N2 - We prove that Chevalley groups over polynomial rings $\mathbb F_q[t]$ and over Laurent polynomial $\mathbb F_q[t,t^{-1}]$ rings, where $\mathbb F_q$ is a finite field, are boundedly elementarily generated. Using this we produce explicit bounds of the commutator width of these groups. Under some additional assumptions, we prove similar results for other classes of Chevalley groups over Dedekind rings of arithmetic rings in positive characteristic. As a corollary, we produce explicit estimates for the commutator width of affine Kac--Moody groups defined over finite fields. The paper contains also a broader discussion of the bounded generation problem for groups of Lie type, some applications and a list of unsolved problems in the field.

AB - We prove that Chevalley groups over polynomial rings $\mathbb F_q[t]$ and over Laurent polynomial $\mathbb F_q[t,t^{-1}]$ rings, where $\mathbb F_q$ is a finite field, are boundedly elementarily generated. Using this we produce explicit bounds of the commutator width of these groups. Under some additional assumptions, we prove similar results for other classes of Chevalley groups over Dedekind rings of arithmetic rings in positive characteristic. As a corollary, we produce explicit estimates for the commutator width of affine Kac--Moody groups defined over finite fields. The paper contains also a broader discussion of the bounded generation problem for groups of Lie type, some applications and a list of unsolved problems in the field.

KW - Chevalley groups

KW - elementary generators

KW - commutators

KW - bounded generation

KW - Dedekind rings of arithmetic type

KW - Chevalley groups

KW - Kac–Moody groups

KW - bounded generation

KW - Polynomial rings

KW - First order rigidity

UR - https://www.researchgate.net/publication/360186542_Bounded_generation_and_commutator_width_of_Chevalley_groups_function_case

U2 - 10.48550/arXiv.2204.10951

DO - 10.48550/arXiv.2204.10951

M3 - Article

VL - 9

JO - European Journal of Mathematics

JF - European Journal of Mathematics

SN - 2199-675X

M1 - 53

ER -

ID: 94653663