Glasgow Mathematical Journal

Research Article

On non-Hurwitz groups and non-congruence subgroups of the modular group

Jeffrey Cohena1

a1 University of Pittsburgh, Pittsburgh, Pennsylvania 15260

In this note homomorphisms of (2, 3, n) = xs3008x, y: x2 = y3 = (xy)n = 1) into PSL3(q) are considered. Of particular interest is (2, 3, 7) whose finite factors are referred to as Hurwitz groups. It is known (see [3]) that for certain q, PSL2(q) is a Hurwitz group, so that one might suppose that PSL3(q) is a natural place to search for new Hurwitz groups. This intuition turns out to be ill-founded, for as we shall see all Hurwitz subgroups of PSL3(q) have already been discovered in [3].

(Received April 19 1979)

(Revised December 10 1979)