On the almost simple automorphism groups of rank 3 graphs | Sciact - Система учета научной деятельности ИМ СО РАН

On the almost simple automorphism groups of rank 3 graphs Научная публикация

Журнал

Proceedings of the Steklov Institute of Mathematics
ISSN: 0081-5438 , E-ISSN: 1531-8605

Вых. Данные

Год: 2025, Том: 329, Номер: 1, Страницы: S270–S285 Страниц : 16 DOI: 10.1134/S0081543825600772

Ключевые слова

almost simple group, 2-closure of permutation group, rank 3 permutation group, rank 3 graph, automorphism group of a graph

Авторы

Ван Ч. ¹ , Vasil’ev A.V. ² , Revin D.O. ^2,3

Организации

1	Hainan University, Haikou, Hainan, China
2	Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
3	Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russia.

Информация о финансировании (1)

Институт математики им. С.Л. Соболева СО РАН

FWNF-2022-0002

A permutation group G of a finite set Ω acts componentwise on the Cartesian square Ω2. The largest subgroup of Sym(Ω) that has the same orbits on Ω2 as G is called the 2-closure of G. The rank of G is the number of its orbits on Ω2. If the rank of G is 3 and the order is even, then an undirected graph with vertex set Ω is defined, up to taking the complement, for which one of the two non-diagonal orbits of G on Ω2 is taken as the edge set. Such a graph is called a rank 3 graph. The full automorphism group of this graph coincides with the 2-closure of G and contains G as a subgroup. At present, with the exception of the case when G is an almost simple group, there exists an explicit description of the 2-closures of rank 3 groups G. In this paper, we fill the existing gap, thereby completing the description of the automorphism groups of rank 3 graphs.

Ван Ч. , Vasil’ev A.V. , Revin D.O.
On the almost simple automorphism groups of rank 3 graphs
Proceedings of the Steklov Institute of Mathematics. 2025. V.329. N1. P.S270–S285. DOI: 10.1134/S0081543825600772 WOS Scopus РИНЦ OpenAlex

Ван Ч. , Васильев А.В. , Ревин Д.О.
О почти простых группах автоморфизмов графов ранга 3
Труды Института математики и механики УрО РАН (Trudy Instituta Matematiki i Mekhaniki UrO RAN). 2025. Т.31. №1. С.36-52. DOI: 10.21538/0134-4889-2025-31-1-fon-04 WOS Scopus РИНЦ OpenAlex

Поступила в редакцию:	12 окт. 2024 г.
Принята к публикации:	9 дек. 2024 г.
Опубликована в печати:	25 мар. 2026 г.
Опубликована online:	25 мар. 2026 г.

≡ Web of science:	WOS:001723279300011
≡ Scopus:	2-s2.0-105033598700
≡ РИНЦ:	89114430
≡ OpenAlex:	W7140321027