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 O2k+1(q), k = 4. As a byproduct, we also obtain (2, 3)-generators for O+ 4k(q) with k = 3 and q odd, and for O± 4k+2(q) with k = 4 and q = ±1 (mod 4).