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

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

Journal

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

Output data

Year: 2026, Volume: 32, Number: 1, Pages: 131–145 Pages count : DOI: 10.21538/0134-4889-2026-32-1-fon-03

Tags

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

Authors

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

Affiliations

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

Funding (1)

Russian Science Foundation

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

Submitted:	Oct 23, 2025
Accepted:	Nov 24, 2025
Published online:	Nov 27, 2025

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