Sciact
  • EN
  • RU

New Examples of Nonpronormal Subgroups of Odd Index in Finite Simple Linear and Unitary Groups Full article

Journal Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260
Output data Year: 2025, Volume: 66, Number: 4, Pages: 928–934 Pages count : 7 DOI: 10.1134/S0037446625040056
Tags finite group, simple group, linear simple group, unitary simple group, pronormal subgroup, odd index
Authors Guo J. 1 , Guo W. 2,3 , Maslova N.V. 4,5 , Revin D.O. 6
Affiliations
1 School of Mathematics and Statistics, Hainan University
2 School of Mathematics and Statistics, Nantong University
3 Department of Mathematics, University of Science and Technology of China
4 Krasovskii Institute of Mathematics and Mechanics
5 Ural Federal University
6 Sobolev Institute of Mathematics

Funding (1)

1 Sobolev Institute of Mathematics FWNF-2022-0002

Abstract: A subgroup H of a group G is said to be pronormal if, for every element g ∈ G, the subgroups H and Hg are conjugate in the subgroup H, Hg . It is known that a substantial portion of finite simple groups possesses property (∗): every subgroup of odd index is pronormal in the group. To date, finite simple groups with property (∗) have been classified, except for finite simple linear and unitary groups subject to certain restrictions on their natural arithmetic parameters. In 2024, a classification was initiated for finite simple linear and unitary groups in which all subgroups of odd index are pronormal. The plan is to identify all possible sources of nonpronormal subgroups of odd index and then prove that there are no other such examples. In 2024, series of examples of nonpronormal subgroups of odd index were found in finite simple linear and unitary groups over fields of odd characteristic. In the present paper, we construct a new series of examples of nonpronormal subgroups of odd index in finite simple linear and unitary groups over a field of odd characteristic.
Cite: Guo J. , Guo W. , Maslova N.V. , Revin D.O.
New Examples of Nonpronormal Subgroups of Odd Index in Finite Simple Linear and Unitary Groups
Siberian Mathematical Journal. 2025. V.66. N4. P.928–934. DOI: 10.1134/S0037446625040056 Scopus РИНЦ OpenAlex
Original: Го Ц. , Го В. , Маслова В. , Ревин Д.О.
Новые примеры непронормальных подгрупп нечетных индексов в конечных простых линейных и унитарных группах
Сибирский математический журнал. 2025. Т.66. №4. С.613-620. DOI: 10.33048/smzh.2025.66.405 РИНЦ
Dates:
Submitted: Dec 27, 2024
Accepted: Apr 25, 2025
Published print: Jul 23, 2025
Published online: Jul 23, 2025
Identifiers:
Scopus: 2-s2.0-105011294291
Elibrary: 82650976
OpenAlex: W4412609974
Citing: Пока нет цитирований
Altmetrics: