Upper bounds for the level of normal subgroups of Hecke groups

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Demirci M., Yurttaş Güneş A., Cangül İ. N.

Numerical Analysis and Applied Mathematics, AIP Conf. Proc., , vol.1389, pp.337-340, 2011 (Peer-Reviewed Journal) identifier


In [4], Greenberg showed that n <= 6t(3) so that mu - nt <= 6t(4) for a normal subgroup N of level n and index mu having t parabolic classes in the modular group Gamma. Accola, [1], improved these to n <= 6t(2) always and n <= t(2) if Gamma/N is not abelian. In this work we generalise these results to Hecke groups. We get results between three parameters of a normal subgroup, i.e. the index mu, the level n and the parabolic class number t. We deal with the case q = 4, and then obtain the generalisation to other q. Two main problems here are the calculation of the number of normal subgroups and the determination of the bounds on the level n for a given t.