Advances in Theoretical and Applied Mathematics
  • Year: 2007
  • Volume: 2
  • Issue: 2

Normal subgroups of the hecke group H (√2) corresponding to one relator quotients of small order

  • Author:
  • Hasan Basri Özdemir1, Yücel Türker Ulutaş2, İsmail Naci Cangül3
  • Total Page Count: 9
  • Page Number: 153 to 161

1Dept. Of Mathematics, Faculty of Education, University of Balıkesir, Balikesir/Turkey, 41100, Kocaeli/Turkey. E-mail: hozdemir@balikesir.edu.tr

2Dept. Of Mathematics, Faculty of Science, University of Kocaeli, Görükle, 16059, bursa/Turkey. E-mail: turkery@kou.edu.tr

3Dept. Of Mathematics, Faculty of Science, University of Uluda&gcaron;, Görükle, 16059, bursa/Turkey. E-mail: cangul@uludag.edu.tr

Abstract

H (√2) is one of the Hecke groups isomorphic to the free product of two finite cyclic groups of orders 2 and 4. Here, some one relator quotient groups of H (√2) of small order are found and the corresponding normal subgroups are listed. It is shown that all finite indexed normal subgroups of H (√2) are He(√2), Y2(√2), Y4(√2), S1(√2), S4(√2), T4(√2), (1).

Keywords

Fuchsian groups, triangle groups, cyclically reduced word, one relator quotient