Şahin, Recep2022-03-172022-03-172004Şahin, R. vd. (2004). “Commutator subgroups of the extended Hecke groups (H)over-bar(lambda(q))”. Czechoslovak Mathematical Journal, 54(1), 253-259.0011-4642https://doi.org/10.1023/B:CMAJ.0000027265.81403.8dhttps://link.springer.com/content/pdf/10.1023/B:CMAJ.0000027265.81403.8d.pdfhttp://hdl.handle.net/11452/25142Hecke groups H(lambda(q)) are the discrete subgroups of PSL(2, R) generated by S(z) = -(z + lambda(q))(-1) and T(z) = -1/z. The commutator subgroup of H(lambda(q)), denoted by H'(lambda(q)), is studied in [2]. It was shown that H'(lambda(q)) is a free group of rank q - 1. Here the extended Hecke groups (H) over bar(lambda(q)), obtained by adjoining R-1(z) = 1/(z) over bar to the generators of H(lambda(q)), are considered. The commutator subgroup of (H) over bar(lambda(q)) is shown to be a free product of two finite cyclic groups. Also it is interesting to note that while in the H(lambda(q)) case, the index of H'(lambda(q)) is changed by q, in the case of (H) over bar(lambda(q)), this number is either 4 for q odd or 8 for q even.eninfo:eu-repo/semantics/openAccessMathematicsHecke groupExtended hecke groupCommutator subgroupArticle0002219475000232-s2.0-4043162142253259541MathematicsHecke Groups; Modular Forms; Graph