Commutator subgroups of the power subgroups of generalized Hecke groups
Let \(p\), \(q\geq 2\) be relatively prime integers and let \(H_{p,q}\) be the generalized Hecke group associated to \(p\) and \(q\). The generalized Hecke group \(H_{p,q}\) is generated by \(X(z)=-(z-\lambda _{p})^{-1}\) and \(Y(z)=-(z+\lambda_{q})^{-1}\) where \(\lambda _{p}=2\cos \frac{\pi }{p}\)...
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| Datum: | 2019 |
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| Sprache: | English |
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Lugansk National Taras Shevchenko University
2019
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oai:ojs.admjournal.luguniv.edu.ua:article-5972019-07-14T19:54:06Z Commutator subgroups of the power subgroups of generalized Hecke groups Koruoğlu, Özden Meral, Taner Sahin, Recep generalized Hecke groups, power subgroups, commutator subgroups 20H10, 11F06 Let \(p\), \(q\geq 2\) be relatively prime integers and let \(H_{p,q}\) be the generalized Hecke group associated to \(p\) and \(q\). The generalized Hecke group \(H_{p,q}\) is generated by \(X(z)=-(z-\lambda _{p})^{-1}\) and \(Y(z)=-(z+\lambda_{q})^{-1}\) where \(\lambda _{p}=2\cos \frac{\pi }{p}\) and \(\lambda_{q}=2\cos \frac{\pi }{q}\). In this paper, for positive integer \(m\), we study the commutator subgroups \((H_{p,q}^{m})'\) of the power subgroups \(H_{p,q}^{m}\) of generalized Hecke groups \(H_{p,q}\). We give an application related with the derived series for all triangle groups of the form \((0;p,q,n)\), for distinct primes \(p\), \(q\) and for positive integer \(n\). Lugansk National Taras Shevchenko University 2019-07-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/597 Algebra and Discrete Mathematics; Vol 27, No 2 (2019) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/597/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/597/284 Copyright (c) 2019 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2019-07-14T19:54:06Z |
| collection |
OJS |
| language |
English |
| topic |
generalized Hecke groups power subgroups commutator subgroups 20H10 11F06 |
| spellingShingle |
generalized Hecke groups power subgroups commutator subgroups 20H10 11F06 Koruoğlu, Özden Meral, Taner Sahin, Recep Commutator subgroups of the power subgroups of generalized Hecke groups |
| topic_facet |
generalized Hecke groups power subgroups commutator subgroups 20H10 11F06 |
| format |
Article |
| author |
Koruoğlu, Özden Meral, Taner Sahin, Recep |
| author_facet |
Koruoğlu, Özden Meral, Taner Sahin, Recep |
| author_sort |
Koruoğlu, Özden |
| title |
Commutator subgroups of the power subgroups of generalized Hecke groups |
| title_short |
Commutator subgroups of the power subgroups of generalized Hecke groups |
| title_full |
Commutator subgroups of the power subgroups of generalized Hecke groups |
| title_fullStr |
Commutator subgroups of the power subgroups of generalized Hecke groups |
| title_full_unstemmed |
Commutator subgroups of the power subgroups of generalized Hecke groups |
| title_sort |
commutator subgroups of the power subgroups of generalized hecke groups |
| description |
Let \(p\), \(q\geq 2\) be relatively prime integers and let \(H_{p,q}\) be the generalized Hecke group associated to \(p\) and \(q\). The generalized Hecke group \(H_{p,q}\) is generated by \(X(z)=-(z-\lambda _{p})^{-1}\) and \(Y(z)=-(z+\lambda_{q})^{-1}\) where \(\lambda _{p}=2\cos \frac{\pi }{p}\) and \(\lambda_{q}=2\cos \frac{\pi }{q}\). In this paper, for positive integer \(m\), we study the commutator subgroups \((H_{p,q}^{m})'\) of the power subgroups \(H_{p,q}^{m}\) of generalized Hecke groups \(H_{p,q}\). We give an application related with the derived series for all triangle groups of the form \((0;p,q,n)\), for distinct primes \(p\), \(q\) and for positive integer \(n\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2019 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/597 |
| work_keys_str_mv |
AT koruogluozden commutatorsubgroupsofthepowersubgroupsofgeneralizedheckegroups AT meraltaner commutatorsubgroupsofthepowersubgroupsofgeneralizedheckegroups AT sahinrecep commutatorsubgroupsofthepowersubgroupsofgeneralizedheckegroups |
| first_indexed |
2025-07-17T10:32:03Z |
| last_indexed |
2025-07-17T10:32:03Z |
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1837889825935458304 |