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Toward the sharp Baer–Suzuki theorem for the π-radical: symplectic groups Научная публикация

Журнал

Algebra and Logic
ISSN: 0002-5232 , E-ISSN: 1573-8302

Вых. Данные

Год: 2025, Том: 64, Номер: 5, Номер статьи : 379–396, Страниц : 18

Ключевые слова

π-radical, π-Baer–Suzuki theorem, finite simple symplectic group.

Авторы

Revin D.O. ^1,2

Организации

1	Novosibirsk State University
2	Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Информация о финансировании (1)

Российский научный фонд

24-11-00127

We study the following conjecture, which is a sharp analogue of the well-known BaerSuzuki theorem for the π-radical of a finite group. For an arbitrary set π of primes not containing all primes, let r be the smallest prime not in π. Setm = r if r ⩽ 3 and m = r−1 if r>3. Then, in a finite group G, the largest normal π-subgroup always coincides with the set of elements x such that any m conjugates of x generate a π-subgroup. To date, this conjecture has been confirmed for any finite group whose every nonabelian composition factor is isomorphic to a sporadic, alternating, linear, or unitary simple group, or to one of the groups 2B2(q), 2G2(q), 2F4(q)′, G2(q), or 3D4(q). It is proved that the simple symplectic groups S2n(q) can be added to this list.

Revin D.O.
Toward the sharp Baer–Suzuki theorem for the π-radical: symplectic groups
Algebra and Logic. 2025. V.64. N5. 379–396 :1-18.

Поступила в редакцию:	18 июн. 2025 г.
Принята к публикации:	11 нояб. 2025 г.

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