Construction of cycloidal free subgroups of hecke groups of finite index

Abstract

Cycloidal subgroups of the modular group are studied in [7]. Cycloidal normal subgroups of the Hecke groups, which are generalisations of the modular group, are studied in [2]. Here we study cycloidal free subgroups of Hecke groups. These are subgroups with signature (g; infinity). Here these subgroups are given by their signatures for q = 4, 5, 6 first, and then for all q. It is found that when q equivalent to 2 mod 4, H(lambda(q)) has no cycloidal free subgroups.