Commutator Subgroups of Generalized Hecke and Extended Generalized Hecke Groups

[1] I. N. Cangül and O. Bizim, Commutator subgroups of Hecke groups, Bull. Inst. Math. Acad. Sinica 30 (2002), no. 4, 253-259.Search in Google Scholar

[2] K. Calta and T. A. Schmidt, Infinitely many lattice surfaces with special pseudo-Anosov maps, J. Mod. Dyn. 7, No. 2, 239-254 (2013).10.3934/jmd.2013.7.239Open DOISearch in Google Scholar

[3] 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/S1446788712000651Search in Google Scholar

[4] Y.H. He and J. Read, Hecke Groups, Dessins d0Enfants and the Archimedean solids, http://arxiv.org/pdf/1309.2326.Search in Google Scholar

[5] E. Hecke, Über die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung, Math. Ann. 112 (1936), 664-699.10.1007/BF01565437Search in Google Scholar

[6] S. Huang, Generalized Hecke groups and Hecke polygons, Ann. Acad. Sci. Fenn., Math. 24, No.1, 187-214 (1999).Search in Google Scholar

[7] S. Huang, Realizability of torsion free subgroups with prescribed signatures in Fuchsian groups, Taiwanese J. Math. 13 (2009), no. 2A, 441-457.10.11650/twjm/1500405348Search in Google Scholar

[8] S. Ikikardes, R. Sahin and I. N. Cangül, Principal congruence subgroups of the Hecke groups and related results, Bull. Braz. Math. Soc. (N.S.) 40, No. 4, 479-494 (2009).10.1007/s00574-009-0023-ySearch in Google Scholar

[9] G. A. Jones, Combinatorial categories and permutation groups, http://arxiv.org/pdf/1309.6119.Search in Google Scholar

[10] R. S. Kulkarni, A new proof and an extension of a theorem of Millington on the modular group, Bull. Lond. Math. Soc. 17, 458-462 (1985).10.1112/blms/17.5.458Search in Google Scholar

[11] J. Lehner, Uniqueness of a class of Fuchsian groups, Illinois J. Math. 19 (1975), 308-315.10.1215/ijm/1256050818Search in Google Scholar

[12] D. Mayer, T. Mühlenbruch and F. Strömberg, The transfer operator for the Hecke triangle groups, Discrete Contin. Dyn. Syst. 32 (2012), no. 7, 2453-2484.10.3934/dcds.2012.32.2453Search in Google Scholar

[13] J. Nielsen, Kommutatorgruppen for det frie produkt af cykliske gruper, Mat. Tidsskr. B (1948), 49-56.Search in Google Scholar

[14] A. D. Pohl, Odd and even Maass cusp forms for Hecke triangle groups, and the billiard ow, http://arxiv.org/pdf/1303.0528.Search in Google Scholar

[15] R. Sahin and O. Bizim, Some subgroups of the extended Hecke groups H( fiq), Acta Math. Sci., Ser. B, Engl. Ed. 23, No.4 (2003), 497-502.10.1016/S0252-9602(17)30493-9Search in Google Scholar

[16] R. Sahin, O. Bizim and I. N. Cangül, Commutator subgroups of the extended Hecke groups, Czech. Math. J. 54, No.1 (2004), 253-259.10.1023/B:CMAJ.0000027265.81403.8dSearch in Google Scholar

[17] R. Sahin, S. Ikikardes and Ö. Koruofiglu, Some normal subgroups of theextended Hecke groups H( fip), Rocky Mountain J. Math. 36 (2006), no. 3, 1033-1048. 10.1216/rmjm/1181069444Search in Google Scholar

[18] R. Sahin and Ö. Koruofiglu, Commutator subgroups of the power subgroups of some Hecke groups, Ramanujan J. 24 (2011), no. 2, 151-159.10.1007/s11139-010-9246-1Open DOISearch in Google Scholar

[19] R. Sahin and Ö. Koruofiglu, Commutator subgroups of the power subgroups of Hecke groups H(q) II, C. R. Math. Acad. Sci. Paris 349 (2011), no. 3-4, 127-130.10.1016/j.crma.2011.01.003Search in Google Scholar

[20] T. A. Schmidt and M. Sheingorn, Covering the Hecke triangle surfaces, Ramanujan J. 1 (1997), no. 2, 155-163.10.1023/A:1009716101565Open DOISearch in Google Scholar

[21] D. Singerman, Subgroups of Fuchsian groups and finite permutation groups, Bull. Lond. Math. Soc. 2, 319-323 (1970).10.1112/blms/2.3.319Open DOISearch in Google Scholar

[22] V. V. Tsanov, Valdemar, Triangle groups, automorphic forms, and torus knots, Enseign. Math. (2) 59 (2013), no. 1-2, 73-113.10.4171/lem/59-1-3Search in Google Scholar