Abstract
Let q >= 3 be an odd integer 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 m-th power subgroup of H(lambda(q)). In this work, the power subgroups H-m(lambda(q)) are discussed. The Reidemeister-Schreier method and the permutation method are used to obtain the abstract group structure and generators of H-m(lambda(q)); their signatures are then also determined. A similar result on the Hecke groups H(lambda(q)), q prime, which says that H'(lambda(q)) congruent to H-2(lambda) boolean AND H-q (lambda(q)), is generalized to Hecke groups H(lambda(q)) with q >= 3 odd integer.