Power and free normal subgroups of generalized Hecke groups

Abstract

Let p and q be integers such that 2 <= p <= q, p + q > 4 and let H-p,H- q be generalized Hecke group associated to p and q. Generalized Hecke group H-p,H- q is generated by X(z) = -(z - lambda(p))(-1) and Y(z) = -(z + lambda(q))(-1), where lambda(p) = 2cos pi/p and lambda(q) = 2cos pi/q. In this paper, for positive integer m, we study the power subgroups H-p,q(m) of generalized Hecke groups H-p,H-q. Also, we give some results about free normal subgroups of generalized Hecke groups H-p,H-q.