On generation by triality automorphisms

2025/08/04 by Revin, Danila O., Zavarnitsine, Andrei V.
#20D06 #20D10 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2508.02277

Abstract

We clarify the structure of subgroups generated by conjugate graph automorphisms of order 3 of O₈⁺(2) and O₈⁺(3). As a result, we obtain a correction to a paper by S. Guest which, in turn, plays an important role in proving the solvable analogue of the Baer--Suzuki theorem.

Citations

• Squares of conjugacy classes and a variant on the Baer-Suzuki Theorem
• Coprime automorphisms of finite groups
• Baer--Suzuki theorem for the π-radical
• On generators and representations of the sporadic simple groups
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• Characterizations of the solvable radical
• A solvable version of the Baer--Suzuki Theorem
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• Generation of finite almost simple groups by conjugates

Related

• Conjugacy classes of trialitarian automorphisms and symmetric compositions
• Triality and Algebraic Groups of Type ³D₄
• An elementary proof of a conjecture on graph-automorphism
• On Basis-Conjugating Automorphisms of Free Groups
• Twisted conjugacy classes of automorphisms of Baumslag-Solitar groups