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Hecke groups are the discrete subgroups of generated by and . The commutator subgroup of (, denoted by , is studied in [2]. It was shown that is a free group of rank . Here the extended Hecke groups , obtained by adjoining to the generators of , are considered. The commutator subgroup of is shown to be a free product of two finite cyclic groups. Also it is interesting to note that while in the case, the index of is changed by , in the case of , this number is either 4 for...
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