On Normal Subgroups of Generalized Hecke Groups

Bilal Demir; Özden Koruoğlu; Recep Sahin

doi:10.1515/auom-2016-0035

.blurhash-client-img { display: none !important; }

On Normal Subgroups of Generalized Hecke Groups

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 24 (2016): Issue 2 (June 2016)

By: Bilal Demir, Özden Koruoğlu and Recep Sahin

Open Access

|Sep 2017

Abstract

We consider the generalized Hecke groups H_p,q generated by X(z) = -(z -λ_p)^-1, Y (z) = -(z +λ_q)^-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 H_p,q defined in [1] and the even subgroup. Then we extend this result to extended generalized Hecke groups H̅_p,q.

References

[1] Ş. Kaymak, B. Demir, Ö. Koruoğlu, R. Sahin, Commutator Subgroups of Generalized Hecke and Extended Generalized Hecke Groups. Submitted.
Search in Google Scholar Back to article
[2] I.N. Cangul and O. Bizim, Normal Subgroups of Hecke Groups on Sphere and Torus, Tr. J. of Mathematics, 22, 369-377, (1998).
Search in Google Scholar Back to article
[3] I.N. Cangul, Normal Subgroups of Hecke Groups, Ph.D. Thesis, Southampton University, (1993).
Search in Google Scholar Back to article
[4] I.N. Cangul, Normal Subgroups and Elements of H0(_q), Tr. J. of Mathematics, 23, 251-256, (1999).
Search in Google Scholar Back to article
[5] I.N. Cangul, O. Bizim, Commutator Subgroups of Hecke Groups, Bull. Inst. Math. Acad. Sinica, 30, 253-259, (2002).
Search in Google Scholar Back to article
[6] R. Sahin, O. Bizim, Some Subgroups of Extended Hecke Groups H(_q), Actua. Math. Sci., 23,(4), 497-502, (2003).10.1016/S0252-9602(17)30493-9
Search in Google Scholar Back to article
[7] R. Sahin, O. Bizim, I.N. Cangul, Commutator Subgroups of the Extended Hecke Groups H(_q), Czech. Math., 28, 253-259, (2004).10.1023/B:CMAJ.0000027265.81403.8d
Search in Google Scholar Back to article
[8] E. Hecke, Über die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung, Math. Ann. 112, 664-699, (1936).10.1007/BF01565437
Search in Google Scholar Back to article
[9] D. Singerman, Finitely Maximal Fuchsian Groups, J. London Math. Soc., (2), 6, 29-38, (1972).10.1112/jlms/s2-6.1.29
Search in Google Scholar Back to article
[10] I.N. Cangul and D. Singerman, Normal Subgroups of Hecke Groups and Regular Maps, Math. Proc. Camb. Phil. Soc. 123, 59, (1998).10.1017/S0305004197002004
Search in Google Scholar Back to article
[11] Lehner, J. and Newman, M., Real Two-Dimensional Representations of the Modular Group and Related Groups, .Amer. J. Math. 87, 945-954, (1965).10.2307/2373255
Search in Google Scholar Back to article
[12] Lehner, J. and Newman, M., Real Two-Dimensional Representations of the Free Product of Two Finite Cyclic Groups, Proc. Camb. Phil. Soc. 62, 135, (1965).10.1017/S0305004100039669
Search in Google Scholar Back to article
[13] J. Lehner, Uniqueness of a class of Fuchsian groups, III. J. Math. Surveys, 8, A.M.S. Providence, R.L. (1964).
Search in Google Scholar Back to article
[14] B. Demir, Ö. Koruoğlu, R. Sahin, Conjugacy Classes of Extended Generalized Hecke Groups. Submitted.
Search in Google Scholar Back to article
[15] K. Calta and T. A. Schmidt, Continued fractions for a class of triangle groups, J. Aust. Math. Soc. 93, No. 1-2, 21-42 (2012).10.1017/S1446788712000651
Search in Google Scholar Back to article
[16] K. Calta and T. A. Schmidt, In_nitely many lattice surfaces with special pseudo-Anosov maps, J. Mod. Dyn. 7, No. 2, 239-254 (2013).10.3934/jmd.2013.7.239
Open DOI Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.1515/auom-2016-0035 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

Journal RSS Feed

Language: English

Page range: 169 - 184

Submitted on: May 7, 2015

Accepted on: Jun 11, 2015

Published on: Sep 21, 2017

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Generalized Hecke groups,

Extended generalized Hecke groups,

Genus 0 normal subgroups,

Even subgroups

Related subjects:

Mathematics,

General mathematics

© 2017 Bilal Demir, Özden Koruoğlu, Recep Sahin, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 24 (2016): Issue 2 (June 2016)