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On the Baer–Suzuki Width of Some Radical Classes. / Guo, Jin; Guo, Wenbin ; Ревин, Данила Олегович et al.

In: Proceedings of the Steklov Institute of Mathematics, Vol. 317, No. S1, 08.2022, p. S90-S97.

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

Harvard

Guo, J, Guo, W, Ревин, ДО & Tyutyanov, V 2022, 'On the Baer–Suzuki Width of Some Radical Classes', Proceedings of the Steklov Institute of Mathematics, vol. 317, no. S1, pp. S90-S97. https://doi.org/10.1134/S0081543822030075

APA

Guo, J., Guo, W., Ревин, Д. О., & Tyutyanov, V. (2022). On the Baer–Suzuki Width of Some Radical Classes. Proceedings of the Steklov Institute of Mathematics, 317(S1), S90-S97. https://doi.org/10.1134/S0081543822030075

Vancouver

Guo J, Guo W, Ревин ДО, Tyutyanov V. On the Baer–Suzuki Width of Some Radical Classes. Proceedings of the Steklov Institute of Mathematics. 2022 Aug;317(S1):S90-S97. doi: 10.1134/S0081543822030075

Author

Guo, Jin ; Guo, Wenbin ; Ревин, Данила Олегович et al. / On the Baer–Suzuki Width of Some Radical Classes. In: Proceedings of the Steklov Institute of Mathematics. 2022 ; Vol. 317, No. S1. pp. S90-S97.

BibTeX

@article{8038697f49a14b4f9858efb43fa9ff1b,
title = "On the Baer–Suzuki Width of Some Radical Classes",
abstract = "Let σ = {σi | i ∈ I} be a fixed partition of the set of all primes into pairwise disjoint nonempty subsets σi. A finite group is called σ-nilpotent if it has a normal σi-Hall subgroup for any i ∈ I. Any finite group possesses a σ-nilpotent radical, which is the largest normal σ-nilpotent subgroup. In this note, it is proved that there exists an integer m = m(σ) such that the σ-nilpotent radical of any finite group coincides with the set of elements x such that any m conjugates of x generate a σ-nilpotent subgroup. Other possible analogs of the classical Baer–Suzuki theorem are discussed.",
keywords = "Baer–Suzuki width, complete class of groups, σ-nilpotent group, σ-solvable group",
author = "Jin Guo and Wenbin Guo and Ревин, {Данила Олегович} and Valentin Tyutyanov",
note = "Funding Agency: J. Guo and W. Guo were supported by the National Natural Science Foundation of China (project nos. 11961017 and 12171126). D.O.Revin and V.N.Tyutyanov were supported by the joint grant of the Russian Foundation for Basic Research (project no. 20-51-00007) and the Belarusian Republican Foundation for Fundamental Research (project no. F20R-291). D. O. Revin was also supported by the Program for Fundamental Research of the Russian Academy of Sciences (project no. FWNF-2022-0002).",
year = "2022",
month = aug,
doi = "10.1134/S0081543822030075",
language = "English",
volume = "317",
pages = "S90--S97",
journal = "Proceedings of the Steklov Institute of Mathematics",
issn = "0081-5438",
publisher = "Maik Nauka Publishing / Springer SBM",
number = "S1",

}

RIS

TY - JOUR

T1 - On the Baer–Suzuki Width of Some Radical Classes

AU - Guo, Jin

AU - Guo, Wenbin

AU - Ревин, Данила Олегович

AU - Tyutyanov, Valentin

N1 - Funding Agency: J. Guo and W. Guo were supported by the National Natural Science Foundation of China (project nos. 11961017 and 12171126). D.O.Revin and V.N.Tyutyanov were supported by the joint grant of the Russian Foundation for Basic Research (project no. 20-51-00007) and the Belarusian Republican Foundation for Fundamental Research (project no. F20R-291). D. O. Revin was also supported by the Program for Fundamental Research of the Russian Academy of Sciences (project no. FWNF-2022-0002).

PY - 2022/8

Y1 - 2022/8

N2 - Let σ = {σi | i ∈ I} be a fixed partition of the set of all primes into pairwise disjoint nonempty subsets σi. A finite group is called σ-nilpotent if it has a normal σi-Hall subgroup for any i ∈ I. Any finite group possesses a σ-nilpotent radical, which is the largest normal σ-nilpotent subgroup. In this note, it is proved that there exists an integer m = m(σ) such that the σ-nilpotent radical of any finite group coincides with the set of elements x such that any m conjugates of x generate a σ-nilpotent subgroup. Other possible analogs of the classical Baer–Suzuki theorem are discussed.

AB - Let σ = {σi | i ∈ I} be a fixed partition of the set of all primes into pairwise disjoint nonempty subsets σi. A finite group is called σ-nilpotent if it has a normal σi-Hall subgroup for any i ∈ I. Any finite group possesses a σ-nilpotent radical, which is the largest normal σ-nilpotent subgroup. In this note, it is proved that there exists an integer m = m(σ) such that the σ-nilpotent radical of any finite group coincides with the set of elements x such that any m conjugates of x generate a σ-nilpotent subgroup. Other possible analogs of the classical Baer–Suzuki theorem are discussed.

KW - Baer–Suzuki width

KW - complete class of groups

KW - σ-nilpotent group

KW - σ-solvable group

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UR - https://www.mendeley.com/catalogue/169fd2fb-792f-3be6-8013-1cb4562d9ab5/

U2 - 10.1134/S0081543822030075

DO - 10.1134/S0081543822030075

M3 - Article

VL - 317

SP - S90-S97

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

SN - 0081-5438

IS - S1

ER -

ID: 42376312