Commutator subgroups of the extended Hecke groups (H)over-bar(lambda(q))

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Date

2004

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Publisher

Springer Heidelberg

Abstract

Hecke 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.

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Keywords

Mathematics, Hecke group, Extended hecke group, Commutator subgroup

Citation

Şahin, R. vd. (2004). “Commutator subgroups of the extended Hecke groups (H)over-bar(lambda(q))”. Czechoslovak Mathematical Journal, 54(1), 253-259.