THE (2,3) -GENERATION OF THE FINITE SIMPLE ODD-DIMENSIONAL ORTHOGONAL GROUPS

The complete classification of the finite simple groups that are $(2,3)$ -generated is a problem which is still open only for orthogonal groups. Here, we construct $(2, 3)$ -generators for the finite odd-dimensional orthogonal groups Ω ₂ₖ₊₁(q) , k≥ 4 . As a byproduct, we also obtain $(2,3)$ -generators for Ω ₄ₖ⁺(q) with k≥ 3 and q odd, and for Ω ₄ₖ₊₂^± (q) with k≥ 4 and q≡ ± 1~ (mod~ 4) .