Upper bounds for the level of normal subgroups of Hecke groups


DEMİRCİ M., YURTTAŞ A. , CANGÜL İ. N.

FRONTIERS OF FUNDAMENTAL AND COMPUTATIONAL PHYSICS, vol.1389, pp.337-340, 2011 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 1389
  • Publication Date: 2011
  • Doi Number: 10.1063/1.3636733
  • Title of Journal : FRONTIERS OF FUNDAMENTAL AND COMPUTATIONAL PHYSICS
  • Page Numbers: pp.337-340

Abstract

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.