Some results on Hecke and extended Hecke groups

Abstract

Let q ≥ 3 be a prime number and let H(λq) be the extended Hecke group associated with q. In this paper, we determine the presentation of the commutator subgroup ( H ( λq)α) ′ of the normal subgroup H ( λq)α , where H ( λq)α is a subgroup of index 2 in H ( λq). Next we discuss the commutator subgroup ( H2) ′ ( λq) of the principal congruence subgroup H2 ( λq) of H ( λq) . Then we show that some quotient groups of H ( λq) are generalized M * − groups. Finally, we prove some results related to some normal subgroups of H ( λq) , especially in the case q = 5.

Some Normal Subgroups of Extended Generalized Hecke Groups

“…For more details please see [13]. Commutator subgroups and power subgroups of Hecke and extended Hecke groups have been studied in, [14], [15], [17], [20], [23], [24] and [25]. Here, our aim is to generalize the results given in [14] and [15] Here, we investigate the cases of p, odd or even, seperately.…”