Geodesic
Nonparabolic subgroups of the modular group
Glasgow mathematical journal, Tome 16 (1975) no. 2, pp. 91-102

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

In this paper we shall discuss maximal nonparabolic and maximal normal nonparabolic subgroups of the modular group Г = 〈ω, φ; ω2 =φ3 = 1〉. The modular group may also be defined as the group of fractional linear transformations w = (az+b)/(cz+d), where a, b, c, d are rational integers with ad − bc = 1. Here, a maximal nonparabolic subgroup of Г is a subgroup that contains no parabolic elements and any proper subgroup of Г which contains S contains parabolic elements. Similarly, a maximal normal nonparabolic subgroup is a normal nonparabolic subgroup of Г which is not contained in any larger normal nonparabolic subgroup of Г. 
Tretkoff, Carol. Nonparabolic subgroups of the modular group. Glasgow mathematical journal, Tome 16 (1975) no. 2, pp. 91-102. doi: 10.1017/S0017089500002573
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