Some normal subgroups of extended generalized Hecke groups

Abstract

Generalized Hecke group H p,∞ (λ) is generated by X(z) = −(z − λ p ) −1
and Y (z) = −(z + λ) −1 where λ p = 2 cos πp , p ≥ 2 integer and λ ≥ 2 .
Extended generalized Hecke group H p,∞ (λ) is obtained by adding the
reection R(z) = 1/z to the generators of generalized Hecke group
H p,∞ (λ). In this paper, we study the commutator subgroups of ex-
tended generalized Hecke groups H p,∞ (λ). Also, we determine the
power subgroups of generalized Hecke groups H p,∞ (λ) and extended
generalized Hecke groups H p,∞ (λ) .

Keywords

• Generalized Hecke groups,Extended generalized Hecke groups,Commutator subgroups,Power subgroups

References

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