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).
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Research Article |
Yazarlar | |
Yayımlanma Tarihi | 1 Ocak 1994 |
Gönderilme Tarihi | 1 Ocak 1994 |
Yayımlandığı Sayı | Yıl 1994 Cilt: 43 |
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
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