- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 43
- Normal subgroups of the Hecke group H (√2)
Normal subgroups of the Hecke group H (√2)
Authors : I. N. Cangül
Pages : 0-0
Doi:10.1501/Commua1_0000000479
View : 6 | Download : 6
Publication Date : 1994-01-01
Article Type : Research
Abstract :Hecke groups H(Z) are the discrete subgroups of PSL(2, R) (the group of orientation preserving isometries of the upper half plane U) generated by two linear fractional transformations R (z) == - 1 / z and T (z) = z + X where XeR, X > 2 or X = Xq = 2cos (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 (Xq) is the free product of two cyclic groups of orders 2 and q, i.e. H (Xq) S C2 * so that the signature of H (Zq) is (O; 2, q, oo).Keywords : Normal subgroups, Hecke group, H (√2)