On the solvable analogue of the Baer–Suzuki theorem and generation by conjugate trialities Full article
| Journal |
Journal of Algebra
ISSN: 0021-8693 , E-ISSN: 1090-266X |
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| Output data | Year: 2026, Volume: 688, Pages: 445–453 Pages count : 9 DOI: 10.1016/j.jalgebra.2025.10.005 | ||
| Tags | Solvable radical, Simple orthogonal group, Triality, Conjugacy, Generators | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Министерство науки и высшего образования РФ | FWNF-2026-0017 |
Abstract:
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).
Cite:
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
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
Dates:
| Submitted: | Aug 5, 2025 |
| Published online: | Oct 10, 2025 |
Identifiers:
| Scopus: | 2-s2.0-105018870141 |
| OpenAlex: | W4415045705 |
Citing:
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