Commutator subgroups of the power subgroups of some Hecke groups. (Q631504)

Commutator subgroups of the power subgroups of some Hecke groups are studied. It is shown that the commutator subgroup of \(H^q(\lambda_q)\) is a free group of rank \(1+(q-1)2^{q-1}\) by using the Reidemeister-Schreier method, where \(q\geq 3\) is a prime. Also the relationships between the derived series of the triangle groups \((0;2,q,n)\) for \(n\) a positive integer and the signatures of some subgroups of \(H(\lambda_q)\) are given.