Quadrangle groups inclusions

  • António Breda d’Azevedo
  • Domenico A. Catalano
  • Ján KarabášEmail author
  • Roman Nedela
Original Paper


In this paper we generalise Singerman’s results on triangle group inclusions to the broader class of generalised quadrangle groups, that is, Fuchsian groups with signature of genus 0 and generated by three or four elliptic generators. For any possible inclusion \(P<Q\) we also give the number of non-conjugate subgroups of Q isomorphic to P.


Fuchsian group Riemann surface Generalised quadrangle group Triangle group Dessin d’enfant 

Mathematics Subject Classification

20H10 30F35 14H57 05E18 



This work was supported by the Research and Development Cooperation project Slovakia–Portugal, ID number: SK-PT-NEWPROJECT-12522, supported by the portuguese side by the Portuguese Foundation for Science and Technology FCT (Fundação para a Ciência e a Tecnologia). The work of the first two authors was partially supported by Portuguese funds through the CIDMA—Center for Research and Development in Mathematics and Applications (University of Aveiro) and FCT within project PEst-OE/MAT/UI4106/2014. The work of of the third and the fourth author was supported by the Ministry of Education of Slovak Republic, Grant VEGA 1/0150/14, Grant APVV-SK-PT-0004-12, and by the Project L01506 of the Czech Ministry of Education, Youth and Sports.


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© The Managing Editors 2016

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade de AveiroAveiroPortugal
  2. 2.Department of Computer ScienceMatej Bel University Faculty of Natural SciencesBanská BystricaSlovakia
  3. 3.Department of MathematicsUniversity of West Bohemia Faculty of Applied SciencesPlzeňCzech Republic

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