On recognition by Gruenberg-Kegel graph of finite nonabelian simple groups with orders having prime divisors at most 13 | Sciact - Система учета научной деятельности ИМ СО РАН

On recognition by Gruenberg-Kegel graph of finite nonabelian simple groups with orders having prime divisors at most 13 Научная публикация

Журнал

Труды Института математики и механики УрО РАН (Trudy Instituta Matematiki i Mekhaniki UrO RAN)
ISSN: 0134-4889 , E-ISSN: 2658-4786

Вых. Данные

Год: 2026, Том: 32, Номер: 1, Страницы: 131–145 Страниц : DOI: 10.21538/0134-4889-2026-32-1-fon-03

Ключевые слова

finite group, simple group, Gruenberg–Kegel graph (prime graph), recognition.

Авторы

Maslova N.V. ^1,2 , Nechitailo L.G. ^3,4

Организации

1	Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090
2	N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620077 Russia
3	Moscow Institute of Physics and Technology, Dolgoprudny, 141701 Russia
4	HSE University, 109028, Moscow, Russia

Информация о финансировании (1)

Российский научный фонд

24-11-00119

The spectrum of a finite group G is the set of all element orders of G. The Gruenberg—Kegel graph (or the prime graph) Γ(G) of a finite group G is defined as follows. The vertex set of Γ(G) is the set of all prime divisors of the order of G. Two distinct primes p and q are adjacent in Γ(G) if and only if there exists an element of order pq in G. We say that the problem of recognition by Gruenberg–Kegel graph (by spectrum, respectively) is solved for a finite group if the number of pairwise non-isomorphic finite groups with the same Gruenberg–Kegel graph (spectrum, respectively) as the group under study is known. In 2005, A.V. Vasil’ev completed solving the problem of recognition by spectrum for all finite nonabelian simple groups with orders having prime divisors at most 13. In this paper we complete the solution of the problem of recognition by Gruenberg–Kegel graph for these groups.

Maslova N.V. , Nechitailo L.G.
On recognition by Gruenberg-Kegel graph of finite nonabelian simple groups with orders having prime divisors at most 13
Труды Института математики и механики УрО РАН (Trudy Instituta Matematiki i Mekhaniki UrO RAN). 2026. V.32. N1. P.131–145. DOI: 10.21538/0134-4889-2026-32-1-fon-03 РИНЦ OpenAlex

Поступила в редакцию:	23 окт. 2025 г.
Принята к публикации:	24 нояб. 2025 г.
Опубликована online:	27 нояб. 2025 г.

≡ РИНЦ:	89058197
≡ OpenAlex:	W4416688382