On schurity of dihedral groups Научная публикация
| Журнал |
Journal of Algebra
ISSN: 0021-8693 , E-ISSN: 1090-266X |
||||
|---|---|---|---|---|---|
| Вых. Данные | Год: 2025, Том: 682, Страницы: 247-277 Страниц : 31 DOI: 10.1016/j.jalgebra.2025.05.035 | ||||
| Ключевые слова | Schur rings, Schur groups, Difference sets, Dihedral groups | ||||
| Авторы |
|
||||
| Организации |
|
Реферат:
A finite group G is called a Schur group if every S-ring over Gis schurian, i.e. associated in a natural way with a subgroup of Sym(G)that contains all right translations. One of the crucial questions in the S-ring theory is the question on schurity of nonabelian groups, in particular, on existence of an infinite family of nonabelian Schur groups. In this paper, we study schurity of dihedral groups. We show that any generalized dihedral Schur group is dihedral and obtain necessary conditions of schurity for dihedral groups. Further, we prove that a dihedral group of order 2p, where p is a Fermat prime or prime of the form p=4q+1, where qis also prime, is Schur. Towards this result, we prove nonexistence of a difference set in a cyclic group of order p ̸=13and classify all S-rings over some dihedral groups.
Библиографическая ссылка:
Ryabov G.
On schurity of dihedral groups
Journal of Algebra. 2025. V.682. P.247-277. DOI: 10.1016/j.jalgebra.2025.05.035 WOS Scopus OpenAlex
On schurity of dihedral groups
Journal of Algebra. 2025. V.682. P.247-277. DOI: 10.1016/j.jalgebra.2025.05.035 WOS Scopus OpenAlex
Даты:
| Поступила в редакцию: | 19 февр. 2025 г. |
| Опубликована online: | 17 июн. 2025 г. |
Идентификаторы БД:
| Web of science: | WOS:001518652600006 |
| Scopus: | 2-s2.0-105008540757 |
| OpenAlex: | W4411371978 |
Цитирование в БД:
Пока нет цитирований