Upper bounds for the level of normal subgroups of Hecke groups
Numerical Analysis and Applied Mathematics, AIP Conf. Proc., , cilt.1389, ss.337-340, 2011 (Hakemli Dergi)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 1389
- Basım Tarihi: 2011
- Doi Numarası: 10.1063/1.3636733
- Dergi Adı: Numerical Analysis and Applied Mathematics, AIP Conf. Proc.,
- Derginin Tarandığı İndeksler: Other Indexes
- Sayfa Sayıları: ss.337-340
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Bursa Uludağ Üniversitesi Adresli: Evet
Özet
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.