On the Baer--Suzuki Width of Some Radical Classes

On the Baer--Suzuki Width of Some Radical Classes Full article

Journal

Proceedings of the Steklov Institute of Mathematics
ISSN: 0081-5438 , E-ISSN: 1531-8605

Output data

Year: 2022, Volume: 217, Number: Suppl. 1, Pages: S90-S97 Pages count : 8 DOI: 10.1134/S0081543822030075

Tags

Baer–Suzuki width, σ-nilpotent group, σ-solvable group, complete class of groups.

Authors

Guo J. ¹ , Guo W. ^1,2 , Revin D.O. ^3,4 , Tyutyanov V.N. ⁵

Affiliations

1	Hainan University, Haikou, 570228 China
2	University of Science and Technology of China, Hefei, 230026 China
3	Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090 Russia
4	Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia
5	Gomel Branch of the International University “MITSO,” Gomel, 246029 Belarus

Funding (2)

1	Sobolev Institute of Mathematics	FWNF-2022-0002
2	Russian Foundation for Basic Research	20-51-00007

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.

Guo J. , Guo W. , Revin D.O. , Tyutyanov V.N.
On the Baer--Suzuki Width of Some Radical Classes
Proceedings of the Steklov Institute of Mathematics. 2022. V.217. NSuppl. 1. P.S90-S97. DOI: 10.1134/S0081543822030075 WOS Scopus РИНЦ OpenAlex

Го Ц. , Го В. , Ревин Д.О. , Тютянов В.Н.
О ширине Бэра - Сузуки некоторых радикальных классов
Труды Института математики и механики УрО РАН (Trudy Instituta Matematiki i Mekhaniki UrO RAN). 2022. Т.28. №2. С.96-105. DOI: 10.21538/0134-4889-2022-28-2-96-105 WOS Scopus РИНЦ OpenAlex

Submitted:	Apr 10, 2022
Accepted:	Apr 25, 2022
Published print:	Nov 14, 2022
Published online:	Nov 14, 2022

Web of science:	WOS:000883773100007
Scopus:	2-s2.0-85145422374
Elibrary:	51824085
OpenAlex:	W4312334726

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