Cycloidal normal subgroups, that is, subgroups with only one cusp, of finite index of Hecke groups, which have been introduced by E. Hecke, and can be thought of as some kind of generalisation of the well-known modular group, are studied. It is shown that they correspond to cyclic quotients of Hecke groups and therefore have non-compact associated Riemann surfaces with a cusp. Finally, their total number have been formulated.
CANGÜL, İSMAİL NACİ and BİZİM, OSMAN (1999) "Cycloidal Normal Subgroups of Hecke Groups of Finite Index," Turkish Journal of Mathematics: Vol. 23: No. 2, Article 12. Available at: https://journals.tubitak.gov.tr/math/vol23/iss2/12