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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2022, Volume 28, Number 2, Pages 96–105
DOI: https://doi.org/10.21538/0134-4889-2022-28-2-96-105
(Mi timm1907)
 

On the Baer–Suzuki Width of Some Radical Classes

J. Guoa, W. Guoab, D. O. Revincd, V. N. Tyutyanove

a School of Science, Hainan University
b University of Science and Technology of China, Anhui, Hefei
c Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
d N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
e Gomel Branch of International University "MITSO"
References:
Abstract: Let $\sigma=\{\sigma_i\mid i\in I\}$ be a fixed partition of the set of all primes into pairwise disjoint nonempty subsets $\sigma_i$. A finite group is called $\sigma$-nilpotent if it has a normal $\sigma_i$-Hall subgroup for any $i\in I$. Any finite group possesses a $\sigma$-nilpotent radical, which is the largest normal $\sigma$-nilpotent subgroup. In this note, it is proved that there exists an integer $m=m(\sigma)$ such that the $\sigma$-nilpotent radical of any finite group coincides with the set of elements $x$ such that any $m$ conjugates of $x$ generate a $\sigma$-nilpotent subgroup. Other possible analogs of the classical Baer–Suzuki theorem are discussed.
Keywords: Baer–Suzuki width, $\sigma$-nilpotent group, $\sigma$-solvable group, complete class of groups.
Funding agency Grant number
National Natural Science Foundation of China 11961017
12171126
Russian Foundation for Basic Research 20-51-00007
Belarusian Republican Foundation for Fundamental Research Ф20Р-291
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0002
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).
Received: 10.04.2022
Revised: 20.04.2022
Accepted: 25.04.2022
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2022, Volume 317, Issue 1, Pages S90–S97
DOI: https://doi.org/10.1134/S0081543822030075
Bibliographic databases:
Document Type: Article
UDC: 517.542
Language: Russian
Citation: J. Guo, W. Guo, D. O. Revin, V. N. Tyutyanov, “On the Baer–Suzuki Width of Some Radical Classes”, Trudy Inst. Mat. i Mekh. UrO RAN, 28, no. 2, 2022, 96–105; Proc. Steklov Inst. Math. (Suppl.), 317, suppl. 1 (2022), S90–S97
Citation in format AMSBIB
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