Narrow Results

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 PSL₃(q), q ≠ 4, and PSU₃(q²), q² ≠ 9, 25. If n = 5 they are PSL₅(q), for all q, and PSU₅(q²), q² ≥ 9. Also, the soluble group PSU₃(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.

In this paper we give explicit $(2,3)$-generators of the finite unitary groups ${\mathrm{\text{SU}}}_6(q^2)$, for all $q$. They fit into a uniform sequence of likely $(2,3)$-generators for all $n\ge 6$.