Let p1, • • • , pn be integers where n ≥ 2 and each pi ≥ 2 . Let also H(p1, • • • , pn) be the generalized Hecke group associated to all pi ≥ 2. In this paper, we study the commutator subgroups H ′ (p1, • • • , pn) and H ′ (p1, • • • , pn) of the generalized Hecke group H(p1, • • • , pn) and the extended generalized Hecke group H(p1, • • • , pn) . We give the generators and the signatures of H ′ (p1, • • • , pn) and H ′ (p1, • • • , pn) .
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