Geodesic
On non-Hurwitz groups and non-congruence subgroups of the modular group
Glasgow mathematical journal, Tome 22 (1981) no. 1, pp. 1-7

Voir la notice de l'article provenant de la source Cambridge University Press

In this note homomorphisms of (2, 3, n) = 〈x, 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]. 
Cohen, Jeffrey. On non-Hurwitz groups and non-congruence subgroups of the modular group. Glasgow mathematical journal, Tome 22 (1981) no. 1, pp. 1-7. doi: 10.1017/S0017089500004419
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[1] 1.Hartley, W. W., Ternary collineation groups, Ann. of Math. 27 (1925), 140–158. Google Scholar | DOI

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[3] 3.Macbeath, A. M., Generators of the linear fractional groups, Proceedings of a Symposium of Pure Mathematics in Number Theory, Vol. XII, Houston (1967), 14–32. Google Scholar

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[5] 5.Newman, Morris, Maximal normal subgroups of the modular group, Proc. Amer. Math. Soc. 19 (1968), 1138–44. Google Scholar | DOI

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