On the sharp Baer–Suzuki theorem for the p-radical of a finite group Full article
| Journal |
Sbornik Mathematics
ISSN: 1064-5616 , E-ISSN: 1468-4802 |
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| Output data | Year: 2023, Volume: 214, Number: 1, Pages: 108-147 Pages count : 40 DOI: 10.4213/sm9698e | ||||||
| Tags | simple linear groups, simple unitary groups, π-radical of a group, Baer-Suzuki π-theorem | ||||||
| Authors |
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| Affiliations |
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Funding (3)
| 1 | Russian Foundation for Basic Research | 20-51-00007 |
| 2 | Sobolev Institute of Mathematics | FWNF-2022-0002 |
| 3 |
Министерство науки и высшего образования РФ Mathematical Center in Akademgorodok |
075-15-2019-1613, 075-15-2022-281 |
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.
Cite:
Yang N.
, Wu Z.
, Revin D.O.
, Vdovin E.P.
On the sharp Baer–Suzuki theorem for the p-radical of a finite group
Sbornik Mathematics. 2023. V.214. N1. P.108-147. DOI: 10.4213/sm9698e WOS Scopus РИНЦ MathNet OpenAlex
On the sharp Baer–Suzuki theorem for the p-radical of a finite group
Sbornik Mathematics. 2023. V.214. N1. P.108-147. DOI: 10.4213/sm9698e WOS Scopus РИНЦ MathNet OpenAlex
Original:
Ян Н.
, У Ч.
, Ревин Д.О.
, Вдовин Е.П.
О точной теореме Бэра–Сузуки для π-радикала конечной группы
Математический сборник. 2023. Т.214. №1. С.113–154. DOI: 10.4213/sm9698 РИНЦ MathNet OpenAlex
О точной теореме Бэра–Сузуки для π-радикала конечной группы
Математический сборник. 2023. Т.214. №1. С.113–154. DOI: 10.4213/sm9698 РИНЦ MathNet OpenAlex
Dates:
| Submitted: | Nov 24, 2021 |
| Published online: | Dec 29, 2022 |
| Published print: | Jul 24, 2023 |
Identifiers:
| Web of science: | WOS:001037692200005 |
| Scopus: | 2-s2.0-85145954115 |
| Elibrary: | 62256438 |
| MathNet: | sm9698 |
| OpenAlex: | W4385197761 |