Scotts formula and Hurwitz groups

This paper continues previous work, based on systematic use of a formula of L. Scott, to detect Hurwitz groups. It closes the problem of determining the finite simple groups contained in $PGL_n(F)$ for $nleq 7$ which are Hurwitz, where $F$ is an algebraically closed field. For the groups $G_2(q)$, $qgeq 5$, and the Janko groups $J_1$ and $J_2$ it provides explicit $(2,3,7)$-generators.

The (2,3)-generation of the special unitary groups of dimension 6

In this paper we give explicit (2,3)-generators of the unitary groups SU_6(q^ 2), for all q. They fit into a uniform sequence of likely (2,3)-generators for all n>= 6.

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

In this paper we determine the classical simple groups of dimension r=3,5 which are (2,3)-generated (the cases r = 2, 4 are known). If r = 3, they are PSL_3(q), q <> 4, and PSU_3(q^2), q^2 <> 9, 25. If r = 5 they are PSL_5(q), for all q, and PSU_5(q^2), q^2 >= 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.