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 Ω + 8 (q) and PΩ + 8 (q) are (2, 3)-generated if and only if q ≥ 4; the groups Ω − 8 (q) and PΩ − 8 (q) are (2, 3)-generated for all q ≥ 2.