On the solvable analogue of the Baer–Suzuki theorem and generation by conjugate trialities | Sciact - Система учета научной деятельности ИМ СО РАН

On the solvable analogue of the Baer–Suzuki theorem and generation by conjugate trialities Научная публикация

Журнал

Journal of Algebra
ISSN: 0021-8693 , E-ISSN: 1090-266X

Вых. Данные

Год: 2026, Том: 688, Страницы: 445–453 Страниц : 9 DOI: 10.1016/j.jalgebra.2025.10.005

Ключевые слова

Solvable radical, Simple orthogonal group, Triality, Conjugacy, Generators

Авторы

Revin Danila O. ¹ , Zavarnitsine Andrei V. ¹

Организации

1	Sobolev Institute of Mathematics, 4, Koptyug av. 630090, Novosibirsk, Russia

Информация о финансировании (1)

Министерство науки и высшего образования РФ

FWNF-2026-0017

We propose a correction to a result by S. Guest which plays an important role in proving the well-known solvable analogue of the Baer–Suzuki theorem. Guest’s result states that, apart from an explicit list of exceptions, given an automorphism x of odd prime order of a nonabelian simple group S, there is always an element g ∈ S such that x and x g together generate a nonsolvable group. We show that, for a correct formulation of Guest’s theorem, the triality automorphism of both O+ 8(2) and O+ 8(3)should be added to the list of exceptions. To this end, we use calculations in GAP to clarify the structure of subgroups generated by conjugate graph automorphisms of order 3of O+ 8(2)and O+ 8(3).

Revin D.O. , Zavarnitsine A.V.
On the solvable analogue of the Baer–Suzuki theorem and generation by conjugate trialities
Journal of Algebra. 2026. V.688. P.445–453. DOI: 10.1016/j.jalgebra.2025.10.005 Scopus OpenAlex

Поступила в редакцию:	5 авг. 2025 г.
Опубликована online:	10 окт. 2025 г.

Scopus:	2-s2.0-105018870141
OpenAlex:	W4415045705

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