Normal subgroups of the Hecke group H (√2)

Authors : İn CANGÜL

Pages : 0-0

Doi:10.1501/Commua1_0000000479

View : 10 | Download : 9

Publication Date : 1994-01-01

Article Type : Research Paper

Abstract :Hecke groups Hinsert ignore into journalissuearticles values(Z); are the discrete subgroups of PSLinsert ignore into journalissuearticles values(2, R); insert ignore into journalissuearticles values(the group of orientation preserving isometries of the upper half plane U); generated by two linear fractional transformations R insert ignore into journalissuearticles values(z); == - 1 / z and T insert ignore into journalissuearticles values(z); = z + X where XeR, X > 2 or X = Xq = 2cos insert ignore into journalissuearticles values(tt j q);, qeN, q > 3^. These values of X are the only ones that give discrete groups, by a theorem of E. Hecke. We are going to be interested in the latter case /. = The element S = RT is then elliptic of order q. It is well-known that H insert ignore into journalissuearticles values(Xq); is the free product of two cyclic groups of orders 2 and q, i.e. H insert ignore into journalissuearticles values(Xq); S C2 * so that the signature of H insert ignore into journalissuearticles values(Zq); is insert ignore into journalissuearticles values(O; 2, q, oo);.
Keywords : Normal subgroups, Hecke group, H √2,