Nonpronormal Subgroups of Odd Index in Finite Simple Linear and Unitary Groups | Sciact - Система учета научной деятельности ИМ СО РАН

Nonpronormal Subgroups of Odd Index in Finite Simple Linear and Unitary Groups Научная публикация

Журнал

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

Вых. Данные

Год: 2024, Том: 325, Номер: S1, Страницы: S114-S122 Страниц : 9 DOI: 10.1134/S0081543824030088

Ключевые слова

finite group, simple group, linear simple group, unitary simple group, pronormal subgroup, odd index.

Авторы

Guo W. ^1,2 , Маслова Н.В. ^3,4 , Ревин Д.О. ^3,5

Организации

1	School of Mathematics and Statistics, Hainan University, Haikou, Hainan 570225, P. R. China
2	Department of Mathematics, University of Science and Technology of China, Hefei 230026, P. R. China
3	Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia
4	Ural Federal University, Yekaterinburg, 620002, Russia
5	Sobolev Institute of Mathematics of the Siberia Branch of the Russian Academy of Sciences, Novosibirsk, 630090 Russia;

Информация о финансировании (2)

1	Институт математики им. С.Л. Соболева СО РАН	FWNF-2022-0002
2	Российский научный фонд	19-71-10067

A subgroup H of a group G is pronormal if, for each g ∈ G, the subgroups H and Hg are conjugate in H,Hg . Most of finite simple groups possess the following property (∗): each subgroup of odd index is pronormal in the group. The conjecture that all finite simple groups possess the property (∗) was established in 2012 in a paper by E.P. Vdovin and the third author based on the analysis of the proof that Hall subgroups are pronormal in finite simple groups. However, the conjecture was disproved in 2016 by A.S. Kondrat’ev together with the second and third authors. In a series of papers by Kondrat’ev and the authors published from 2015 to 2020, the finite simple groups with the property (∗) except finite simple linear and unitary groups with some constraints on natural arithmetic parameters were classified. In this paper, we construct series of examples of nonpronormal subgroups of odd index in finite simple linear and unitary groups over a field of odd characteristic, thereby making a step towards completing the classification of finite simple groups with the property (∗).

Guo W. , Маслова Н.В. , Ревин Д.О.
Nonpronormal Subgroups of Odd Index in Finite Simple Linear and Unitary Groups
Proceedings of the Steklov Institute of Mathematics. 2024. V.325. NS1. P.S114-S122. DOI: 10.1134/S0081543824030088 WOS Scopus РИНЦ OpenAlex

Го В. , Маслова Н.В. , Ревин Д.О.
Непронормальные подгруппы нечетных индексов в конечных простых линейных и унитарных группах
Труды Института математики и механики УрО РАН (Trudy Instituta Matematiki i Mekhaniki UrO RAN). 2024. Т.30. №1. С.70-79. DOI: 10.21538/0134-4889-2024-30-1-70-79 WOS Scopus РИНЦ OpenAlex

Поступила в редакцию:	5 дек. 2023 г.
Принята к публикации:	15 янв. 2024 г.
Опубликована в печати:	20 авг. 2024 г.
Опубликована online:	20 авг. 2024 г.

Web of science:	WOS:001295088800015
Scopus:	2-s2.0-85201972158
РИНЦ:	68611676
OpenAlex:	W4401765793

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