The simple classical groups of dimension less than 6 which are (2,3)-generated

Abstract

In this paper, we determine the finite classical simple groups of dimension n = 3, 5 which are (2, 3)-generated (the cases n = 2, 4 are known). If n = 3, they are PSL 3(q), q ≠ 4, and PSU 3(q2), q2 ≠ 9, 25. If n = 5 they are PSL 5(q), for all q, and PSU 5(q2), q2 ≥ 9. Also, the soluble group PSU 3(4) is not (2, 3)-generated. We give explicit (2, 3)-generators of the linear preimages, in the special linear groups, of the (2, 3)-generated simple groups.