Turkish Journal of Mathematics
DOI
-
Abstract
We use regular map theory to obtain all normal subgroups of Hecke groups of genus 0 and 1. The existence of a regular map corresponding uniquely to every normal subgroup of Hecke groups H(\lambda_q) is a result of Jones and Singerman, and it is frequently used here to obtain normal subgroups. It is found that when q is even, H(\lambda_q) has infinitely many normal subgroups on the sphere, while for odd q, this number is finite. The total number of normal subgroups of H(\lambda_q) on a torus is found to be either 0 or infinite. The latter case appears iff q is a multiple of 4. Finally, a result of Rosenberger and Kern-Isberner is reproved here.
Keywords
Hecke groups, genus, regular maps
First Page
369
Last Page
378
Recommended Citation
CANGÜL, İSMAİL NACİ and BİZİM, OSMAN (1998) "Normal Subgroups of hecke Groups on Sphere and," Turkish Journal of Mathematics: Vol. 22: No. 4, Article 2. Available at: https://journals.tubitak.gov.tr/math/vol22/iss4/2
