On characterization by Gruenberg–Kegel graph of finite simple exceptional groups of Lie type
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
On characterization by Gruenberg–Kegel graph of finite simple exceptional groups of Lie type
|
|
| Автор |
Maslova, N. V.
Panshin, V. V. Staroletov, A. M. |
|
| Тематика |
EXCEPTIONAL GROUP OF LIE TYPE
FINITE GROUP GRUENBERG–KEGEL GRAPH (PRIME GRAPH) RECOGNITION BY GRUENBERG–KEGEL GRAPH SIMPLE GROUP |
|
| Описание |
The Gruenberg–Kegel graph (or the prime graph) Γ (G) of a finite group G is the graph whose vertex set is the set of prime divisors of |G| and in which two distinct vertices r and s are adjacent if and only if there exists an element of order rs in G. A finite group G is called almost recognizable (by Gruenberg–Kegel graph) if there is only a finite number of pairwise non-isomorphic finite groups having Gruenberg–Kegel graph as G. If G is not almost recognizable, then it is called unrecognizable (by Gruenberg–Kegel graph). Recently Peter J. Cameron and the first author have proved that if a finite group is almost recognizable, then the group is almost simple. Thus, the question of which almost simple groups (in particular, finite simple groups) are almost recognizable is of prime interest. We prove that every finite simple exceptional group of Lie type, which is isomorphic to neither [InlineEquation not available: see fulltext.] with n⩾ 1 nor G2(3) and whose Gruenberg–Kegel graph has at least three connected components, is almost recognizable. Moreover, groups [InlineEquation not available: see fulltext.], where n⩾ 1 , and G2(3) are unrecognizable. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
075-15-2022-281; FWNF-2022-0002; Ministry of Education and Science of the Russian Federation, Minobrnauka: 075-02-2023-935 The first author is supported by the Ministry of Science and Higher Education of the Russian Federation, project 075-02-2023-935 for the development of the regional scientific and educational mathematical center “Ural Mathematical Center” (Sect. ). The second author is supported by the Mathematical Center in Akademgorodok under the agreement No. 075-15-2022-281 with the Ministry of Science and Higher Education of the Russian Federation (Sect. ). The third author is supported by RAS Fundamental Research Program, project FWNF-2022-0002 (Sect. ). |
|
| Дата |
2024-04-05T16:31:39Z
2024-04-05T16:31:39Z 2023 |
|
| Тип |
Article
Journal article (info:eu-repo/semantics/article) |info:eu-repo/semantics/submittedVersion |
|
| Идентификатор |
Maslova, NV, Panshin, VV & Staroletov, AM 2023, 'On characterization by Gruenberg–Kegel graph of finite simple exceptional groups of Lie type', European Journal of Mathematics, Том. 9, № 3, 78. https://doi.org/10.1007/s40879-023-00672-7
Maslova, N. V., Panshin, V. V., & Staroletov, A. M. (2023). On characterization by Gruenberg–Kegel graph of finite simple exceptional groups of Lie type. European Journal of Mathematics, 9(3), [78]. https://doi.org/10.1007/s40879-023-00672-7 2199-675X Final All Open Access, Green https://www.scopus.com/inward/record.uri?eid=2-s2.0-85168680047&doi=10.1007%2fs40879-023-00672-7&partnerID=40&md5=0dc3fe8b762e76dc747663b160b0945e https://www.researchsquare.com/article/rs-2546565/latest.pdf http://elar.urfu.ru/handle/10995/130731 10.1007/s40879-023-00672-7 85168680047 001053799100001 |
|
| Язык |
en
|
|
| Права |
Open access (info:eu-repo/semantics/openAccess)
cc-by https://creativecommons.org/licenses/by/4.0/ |
|
| Формат |
application/pdf
|
|
| Издатель |
Springer Science and Business Media Deutschland GmbH
|
|
| Источник |
European Journal of Mathematics
European Journal of Mathematics |
|