<abstract xmlns="http://www.w3.org/1999/xhtml"> We consider the generalized Hecke groups Hp,q generated by X(z) = -(z -λp)-1, Y (z) = -(z +λq)-1 with <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/auom-2016-0035_001.jpg"></inline-graphic> and <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/auom-2016-0035_002.jpg"></inline-graphic> where 2 ≤ p ≤ q &lt; ∞, 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 <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/auom-2016-0035_003.jpg"></inline-graphic>. 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. </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.

On Normal Subgroups of Generalized Hecke Groups

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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{"article-title":"On Normal Subgroups of Generalized Hecke Groups"}

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  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.

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...

On Normal Subgroups of Generalized Hecke Groups

Published Online: Sep 21, 2017

Page range: 169 - 184

Received: May 07, 2015

Accepted: Jun 11, 2015

DOI: https://doi.org/10.1515/auom-2016-0035

Keywords
Generalized Hecke groups, Extended generalized Hecke groups, Genus 0 normal subgroups, Even subgroups

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

On Normal Subgroups of Generalized Hecke Groups

Published Online: Sep 21, 2017

Page range: 169 - 184

Received: May 07, 2015

Accepted: Jun 11, 2015

DOI: https://doi.org/10.1515/auom-2016-0035

KeywordsGeneralized Hecke groups, Extended generalized Hecke groups, Genus 0 normal subgroups, Even subgroups

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Generalized Hecke groups, Extended generalized Hecke groups, Genus 0 normal subgroups, Even subgroups