On the sharp Baer-Suzuki theorem for the π-radical of a finite group

Standard

On the sharp Baer-Suzuki theorem for the π-radical of a finite group. / Yang, N.; Wu, Zh; Revin, D. O. и др.

в: Sbornik Mathematics, Том 214, № 1, 2023, стр. 108-147.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Author

Yang, N. ; Wu, Zh ; Revin, D. O. и др. / On the sharp Baer-Suzuki theorem for the π-radical of a finite group. в: Sbornik Mathematics. 2023 ; Том 214, № 1. стр. 108-147.

BibTeX

@article{a0d43b15e54948b39503b24a5084017b,

title = "On the sharp Baer-Suzuki theorem for the π-radical of a finite group",

abstract = "Let π be a proper subset of the set of prime numbers. Denote by r the least prime not contained in π and set m = r for r = 2 and 3 and m = r −1 for r ⩾ 5. The conjecture under consideration claims that a conjugacy class D of a finite group G generates a π-subgroup of G (equivalently, is contained in the π-radical) if and only if any m elements of D generate a π-group. It is shown that this conjecture holds if every non-Abelian composition factor of G is isomorphic to a sporadic, an alternating, a linear, or a unitary simple group.",

keywords = "Baer-Suzuki π-theorem, simple linear groups, simple unitary groups, π-radical of a group",

author = "N. Yang and Zh Wu and Revin, {D. O.} and Vdovin, {E. P.}",

note = "Zh. Wu{\textquoteright}s research was supported by the Natural Science Foundation of Jiangsu Province (grant no. BK20210442) and Jiangsu Shuangchuang (Mass Innovation and Entrepreneurship) Talent Program (grant no. JSSCBS20210841). The research of D. O. Revin was supported by the Russian Foundation for Basic Research and the Belarusian Republican Foundation for Basic Research (grant no. 20-51-00007-Бел_а) and by the Ministry of Education and Science of the Russian Federation within the framework of the state assignment for the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences (project no. FWNF-2022-0002). The work of E. P. Vdovin was carried out at the Mathematical Center in Akademgorodok with the support of the Russian Ministry of Education and Science (agreement no. 075-15-2022-281). AMS 2020 Mathematics Subject Classification. Primary 20D20; Secondary 20D06, 20D08.",

year = "2023",

doi = "10.4213/sm9698e",

language = "English",

volume = "214",

pages = "108--147",

journal = "Sbornik Mathematics",

issn = "1064-5616",

publisher = "Turpion Ltd.",

number = "1",

}

RIS

TY - JOUR

T1 - On the sharp Baer-Suzuki theorem for the π-radical of a finite group

AU - Yang, N.

AU - Wu, Zh

AU - Revin, D. O.

AU - Vdovin, E. P.

N1 - Zh. Wu’s research was supported by the Natural Science Foundation of Jiangsu Province (grant no. BK20210442) and Jiangsu Shuangchuang (Mass Innovation and Entrepreneurship) Talent Program (grant no. JSSCBS20210841). The research of D. O. Revin was supported by the Russian Foundation for Basic Research and the Belarusian Republican Foundation for Basic Research (grant no. 20-51-00007-Бел_а) and by the Ministry of Education and Science of the Russian Federation within the framework of the state assignment for the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences (project no. FWNF-2022-0002). The work of E. P. Vdovin was carried out at the Mathematical Center in Akademgorodok with the support of the Russian Ministry of Education and Science (agreement no. 075-15-2022-281). AMS 2020 Mathematics Subject Classification. Primary 20D20; Secondary 20D06, 20D08.

PY - 2023

Y1 - 2023

N2 - Let π be a proper subset of the set of prime numbers. Denote by r the least prime not contained in π and set m = r for r = 2 and 3 and m = r −1 for r ⩾ 5. The conjecture under consideration claims that a conjugacy class D of a finite group G generates a π-subgroup of G (equivalently, is contained in the π-radical) if and only if any m elements of D generate a π-group. It is shown that this conjecture holds if every non-Abelian composition factor of G is isomorphic to a sporadic, an alternating, a linear, or a unitary simple group.

AB - Let π be a proper subset of the set of prime numbers. Denote by r the least prime not contained in π and set m = r for r = 2 and 3 and m = r −1 for r ⩾ 5. The conjecture under consideration claims that a conjugacy class D of a finite group G generates a π-subgroup of G (equivalently, is contained in the π-radical) if and only if any m elements of D generate a π-group. It is shown that this conjecture holds if every non-Abelian composition factor of G is isomorphic to a sporadic, an alternating, a linear, or a unitary simple group.

KW - Baer-Suzuki π-theorem

KW - simple linear groups

KW - simple unitary groups

KW - π-radical of a group

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85145954115&origin=inward&txGid=7d5e62d747db0b7c07af5a74dd4f5f17

UR - https://www.mendeley.com/catalogue/40b154ad-7606-36b8-bbc0-39ea3cd7f20d/

U2 - 10.4213/sm9698e

DO - 10.4213/sm9698e

M3 - Article

VL - 214

SP - 108

EP - 147

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 1

ER -

ID: 55560457