On maximal nonparabolic normal subgroups of the modular group

Abstract

Let F be a free normal subgroup of finite index in the modular group Γ \Gamma with F ≠ Γ ′ . F ′ F \ne \Gamma ’.F’ is known to be a nonparabolic normal subgroup of Γ \Gamma . We show that, with two exceptions, there exists another nonparabolic normal subgroup of Γ \Gamma properly containing F ′ F’ .