Some normal subgroups of extended generalized Hecke groups

Authors : Bilal DEMİR, Özden KORUOĞLU, Recep ŞAHİN

Pages : 1023-1032

View : 16 | Download : 4

Publication Date : 2016-08-01

Article Type : Research Paper

Abstract :Generalized Hecke group H p,∞ insert ignore into journalissuearticles values(λ); is generated by Xinsert ignore into journalissuearticles values(z); = −insert ignore into journalissuearticles values(z − λ p ); −1 and Y insert ignore into journalissuearticles values(z); = −insert ignore into journalissuearticles values(z + λ); −1 where λ p = 2 cos πp , p ≥ 2 integer and λ ≥ 2 . Extended generalized Hecke group H p,∞ insert ignore into journalissuearticles values(λ); is obtained by adding the reection Rinsert ignore into journalissuearticles values(z); = 1/z to the generators of generalized Hecke group H p,∞ insert ignore into journalissuearticles values(λ);. In this paper, we study the commutator subgroups of ex- tended generalized Hecke groups H p,∞ insert ignore into journalissuearticles values(λ);. Also, we determine the power subgroups of generalized Hecke groups H p,∞ insert ignore into journalissuearticles values(λ); and extended generalized Hecke groups H p,∞ insert ignore into journalissuearticles values(λ); .
Keywords : Generalized Hecke groups, Extended generalized Hecke groups, Commutator subgroups, Power subgroups