Some results on hecke and extended hecke groups

Abstract

Let q >= 3 be a prime number and let (H) over bar(lambda(q)) be the extended Hecke group associated with q. In this paper, we determine the presentation of the commutator subgroup (H (lambda(q))alpha)' of the normal subgroup H (lambda(q)) alpha, where H (lambda(q) )alpha is a subgroup of index 2 in (H) over bar(lambda(q)). Next we discuss the commutator subgroup ((H) over bar (2))' (lambda(q)) of the principal congruence subgroup (H) over bar (2) (lambda(q)) of (H) over bar (lambda(q)) . Then we show that some quotient groups of (H) over bar (lambda(q)) are generalized M*-groups. Finally, we prove some results related to some normal subgroups of (H) over bar (lambda(q)), especially in the case q = 5.