On generation by triality automorphisms

Abstract

We clarify the structure of subgroups generated by conjugate graph automorphisms of order $3$ of $O_8^{+}(2)$ and $O_8^{+}(3)$. 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.