Notes on B -groups Научная публикация
| Журнал |
Communications in Algebra
ISSN: 0092-7872 , E-ISSN: 1532-4125 |
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| Вых. Данные | Год: 2025, Номер: 53, Страницы: 4398–4402 Страниц : 6 DOI: 10.1080/00927872.2025.2484425 | ||||||
| Ключевые слова | Permutation groups, Schur rings, Cayley graphs | ||||||
| Авторы |
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Реферат:
Following Wielandt, a finite group G is called a B-group (Burnside group) if every primitive group containing a regular subgroup isomorphic to G is doubly transitive. Using a method of Schur rings, Wielandt proved that every abelian group of composite order which has at least one cyclic Sylow subgroup is a B group. Since then, other infinite families of B-groups were found by the same method. A simple analysis of the proofs of these results shows that in all of them a stronger statement was proved for the group G under consideration: everyprimitiveSchurringoverGistrivial.AfinitegroupGpossessingthelatter property, we call BS-group (Burnside-Schurgroup). In the present note, we give infinitely many examples of B-groups which are not BS-groups.
Библиографическая ссылка:
Ponomarenko I.
, Ryabov G.
Notes on B -groups
Communications in Algebra. 2025. N53. P.4398–4402. DOI: 10.1080/00927872.2025.2484425 WOS Scopus OpenAlex
Notes on B -groups
Communications in Algebra. 2025. N53. P.4398–4402. DOI: 10.1080/00927872.2025.2484425 WOS Scopus OpenAlex
Даты:
| Поступила в редакцию: | 30 окт. 2024 г. |
| Принята к публикации: | 17 мар. 2025 г. |
| Опубликована online: | 21 апр. 2025 г. |
Идентификаторы БД:
| Web of science: | WOS:001471238300001 |
| Scopus: | 2-s2.0-105003228188 |
| OpenAlex: | W4409625239 |