On Normal Subgroups of Generalized Hecke Groups-Reference-Cited by-同舟云学术

On Normal Subgroups of Generalized Hecke Groups

Published:2016-06-01 Issue:2 Volume:24 Page:169-184
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
language:en
Short-container-title:

Author:

Demir Bilal¹,Koruoğlu Özden¹,Sahin Recep²

Affiliation:

1. Necatibey Faculty of Education, Department of Secondary Mathematics Education, Balıkesir University, 10100 Balıkesir , Turkey

2. Faculty of Science and Arts, Department of Mathematics, Balıkesir University, 10145 Çağış Campus, Balıkesir , Turkey

Abstract

Abstract We consider the generalized Hecke groups Hp,q generated by X(z) = -(z -λp)-1, Y (z) = -(z +λq)-1 with and where 2 ≤ p ≤ q < ∞, p+q > 4. In this work we study the structure of genus 0 normal subgroups of generalized Hecke groups. We construct an interesting genus 0 subgroup called even subgroup, denoted by . We state the relation between commutator subgroup H′p,q of Hp,q defined in [1] and the even subgroup. Then we extend this result to extended generalized Hecke groups H̅p,q.

Publisher

Walter de Gruyter GmbH

Reference16 articles.

1. [1] Ş. Kaymak, B. Demir, Ö. Koruoğlu, R. Sahin, Commutator Subgroups of Generalized Hecke and Extended Generalized Hecke Groups. Submitted.

2. [2] I.N. Cangul and O. Bizim, Normal Subgroups of Hecke Groups on Sphere and Torus, Tr. J. of Mathematics, 22, 369-377, (1998).

3. [3] I.N. Cangul, Normal Subgroups of Hecke Groups, Ph.D. Thesis, Southampton University, (1993).

4. [4] I.N. Cangul, Normal Subgroups and Elements of H0(_q), Tr. J. of Mathematics, 23, 251-256, (1999).

5. [5] I.N. Cangul, O. Bizim, Commutator Subgroups of Hecke Groups, Bull. Inst. Math. Acad. Sinica, 30, 253-259, (2002).

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