Toward a Sharp Baer-Suzuki Theorem for the π-Radical: Exeptional Groups of Small Rank Full article
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Algebra and Logic
ISSN: 0002-5232 , E-ISSN: 1573-8302 |
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| Output data | Year: 2023, Volume: 62, Number: 1, Pages: 1-21 Pages count : 21 DOI: 10.1007/s10469-023-09720-3 | ||||
| Tags | exceptional groups of Lie type, groups 2B2(q), 2G2(q), G2(q), 3D4(q), π-radical of group, Baer–Suzuki π-theorem | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0002 |
Abstract:
Let π be a proper subset of the set of all prime numbers. Denote by r the least prime number not in π, and put m = r, if r = 2, 3, and m = r − 1 if r ≥ 5. We look at the conjecture that a conjugacy class D in a finite group G generates a π-subgroup in G (or, equivalently, is contained in the π-radical) iff any m elements from D generate a π-group. Previously, this conjecture was confirmed for finite groups whose every non-Abelian composition factor is isomorphic to a sporadic, alternating, linear or unitary simple group. Now it is confirmed for groups the list of composition factors of which is added up by exceptional groups of Lie type 2B2(q), 2G2(q), G2(q), and 3D4(q)
Cite:
Wang Z.
, Guo W.
, Revin D.O.
Toward a Sharp Baer-Suzuki Theorem for the π-Radical: Exeptional Groups of Small Rank
Algebra and Logic. 2023. V.62. N1. P.1-21. DOI: 10.1007/s10469-023-09720-3 WOS Scopus РИНЦ OpenAlex
Toward a Sharp Baer-Suzuki Theorem for the π-Radical: Exeptional Groups of Small Rank
Algebra and Logic. 2023. V.62. N1. P.1-21. DOI: 10.1007/s10469-023-09720-3 WOS Scopus РИНЦ OpenAlex
Original:
Ван Ч.
, Го В.
, Ревин Д.О.
К точной теореме Бэра–Судзуки для π-радикала: исключительные группы малого ранга
Алгебра и логика. 2023. Т.62. №1. С.3-32. DOI: 10.33048/alglog.2023.62.101 РИНЦ
К точной теореме Бэра–Судзуки для π-радикала: исключительные группы малого ранга
Алгебра и логика. 2023. Т.62. №1. С.3-32. DOI: 10.33048/alglog.2023.62.101 РИНЦ
Dates:
| Submitted: | Dec 16, 2022 |
| Published print: | Mar 23, 2023 |
| Accepted: | Oct 30, 2023 |
| Published online: | Jan 4, 2024 |
Identifiers:
| Web of science: | WOS:001139076400005 |
| Scopus: | 2-s2.0-85181500697 |
| Elibrary: | 65519032 |
| OpenAlex: | W4390585137 |