Conjugacy classes of extended generalized hecke groups

Abstract

Generalized Hecke groups lip,q are generated by X(z) = (z lambda(p))(-1) and Y(z) = -(z + lambda(q))(-1), where lambda(p) = 2 cos pi/p lambda q= 2 cos pi/q p,q are integers such that 2 <= p <= q, p q > 4. Extended generalized Hecke groups I I p,q are obtained by adding the reflection R(z) = to the generators of generalized Hecke groups lip,q. We determine the conjugacy classes of the torsion elements in extended generalized Hecke groups H p,q.