On characterization by Gruenberg–Kegel graph of finite simple exceptional groups of Lie type Full article
| Journal |
European Journal of Mathematics
ISSN: 2199-675X , E-ISSN: 2199-6768 |
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| Output data | Year: 2023, Volume: 9, Number: 3, Article number : 78, Pages count : 17 DOI: 10.1007/s40879-023-00672-7 | ||||||||
| Tags | Finite group · Simple group · Exceptional group of Lie type · Gruenberg–Kegel graph (prime graph) · Recognition by Gruenberg–Kegel graph | ||||||||
| Authors |
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| Affiliations |
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Funding (2)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0002 |
| 2 |
Министерство науки и высшего образования РФ Mathematical Center in Akademgorodok |
075-15-2019-1613, 075-15-2022-281 |
Abstract:
The Gruenberg–Kegel graph(ortheprimegraph) (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 areadjacent if and only if there exists an element of orderrsin G. A finite group G is called almost recognizable (by Gruenberg–Kegel graph) if there is only a finite number of pairwisenon-isomorphic finite groups having Gruenberg–Kegel graphas 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 primeinterest. We prove that every finite simple exceptional group of Lie type, which is isomorphic to neither 2B2(22n+1) with n ⩾ 1 nor G2(3) and whose Gruenberg–Kegel
Cite:
Maslova N.V.
, Panshin V.V.
, Staroletov A.
On characterization by Gruenberg–Kegel graph of finite simple exceptional groups of Lie type
European Journal of Mathematics. 2023. V.9. N3. 78 :1-17. DOI: 10.1007/s40879-023-00672-7 WOS Scopus РИНЦ OpenAlex
On characterization by Gruenberg–Kegel graph of finite simple exceptional groups of Lie type
European Journal of Mathematics. 2023. V.9. N3. 78 :1-17. DOI: 10.1007/s40879-023-00672-7 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Feb 3, 2023 |
| Accepted: | Jul 18, 2023 |
| Published print: | Aug 23, 2023 |
| Published online: | Aug 23, 2023 |
Identifiers:
| Web of science: | WOS:001053799100001 |
| Scopus: | 2-s2.0-85168680047 |
| Elibrary: | 63302294 |
| OpenAlex: | W4386091275 |