The (2,3)-generation of the finite 8-dimensional orthogonal groups

Abstract

We construct $(2,3)$-generators for the finite $8$-dimensional orthogonal groups, proving the following results: the groups ${\Omega }_8^{+}(q)$ and $P{\Omega }_8^{+}(q)$ are $(2,3)$-generated if and only if $q\ge 4$; the groups ${\Omega }_8^{-}(q)$ and $P{\Omega }_8^{-}(q)$ are $(2,3)$-generated for all $q\ge 2$.