A method for finding normal subgroups of Hecke groups
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Hecke groups, being discrete groups, play an important role in abstract group theory and number theory. Their normal subgroups are studied in [2]: Here, using a result of D. Singerman [7]; we deduce a method of nding normal subgroups of all Hecke groups. This method helps us to obtain the signature of these subgroups, and their abstract group structure can be obtained from this by means of the results in [1]: As a result, the abstract group structure of normal subgroups of Hecke groups corresponding to cyclic and dihedral quotients is obtained.1
Abstract
Hecke groups, being discrete groups, play an important role in abstract group theory and number theory. Their normal subgroups are studied in [2]: Here, using a result of D. Singerman [7]; we deduce a method of nding normal subgroups of all Hecke groups. This method helps us to obtain the signature of these subgroups, and their abstract group structure can be obtained from this by means of the results in [1]: As a result, the abstract group structure of normal subgroups of Hecke groups corresponding to cyclic and dihedral quotients is obtained.1