Commutator subgroups of the power subgroups of some Hecke groups

Abstract

Let qa parts per thousand yen3 be a prime and let H(lambda (q) ) be the Hecke group associated to q. Let m be a positive integer and H (m) (lambda (q) ) be the mth power subgroup of H(lambda (q) ). In this work, we study the commutator subgroups of the power subgroups H (m) (lambda (q) ) of H(lambda (q) ). Then, we give the derived series for all triangle groups of the form (0;2,q,n) for n a positive integer, since there is a nice connection between the signatures of the subgroups we studied and the signatures of these derived series.