The normal subgroup structure of the extended Hecke groups

被引：4

作者：

Koruoglu, Oezden ^{[1
]}

Sahin, Recep

Ikikardes, Sebahattin

机构：

[1] Balikesir Univ, Necatibey Egitim Fak, TR-10100 Balikesir, Turkey

[2] Balikesir Univ, Fen Edebiyat Fak, TR-10145 Balikesir, Turkey

来源：

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY | 2007年 / 38卷 / 01期

关键词：

extended Hecke group; fundamental region; commutator subgroup; even subgroup; power subgroup; SERIES;

D O I：

10.1007/s00574-007-0035-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the extended Hecke groups (H) over bar(lambda) generated by T (z) = -1/z, S(z) = -1/(z + lambda) and R(z) = 1/(z) over bar with lambda >= 2. In this paper, firstly, we study the fundamental region of the extended Hecke groups (H) over bar(lambda). Then, we determine the abstract group structure of the commutator subgroups (H) over bar' (lambda), the even subgroup (H) over bar (e)(lambda), and the power subgroups (H) over bar (m)(lambda) of the extended Hecke groups (H) over bar(lambda). Also, finally, we give some relations between them.

引用

页码：51 / 65

页数：15

共 26 条

[1]

AKBAS M, 1992, LOND MATH S, V173, P1, DOI 10.1017/CBO9780511565793.002

[2] Normal subgroups of Hecke groups and regular maps [J].

Cangul, IN ;

Singerman, D .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1998, 123 :59-74

[3]

CANGUL IN, 1996, TURKISH J MATH, V20, P203

[4]

CONDER M, 2003, U AUCKLAND MATH DEP, V496

[5] THE NORMAL SUBGROUP STRUCTURE OF THE PICARD GROUP [J].

FINE, B ;

NEWMAN, M .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 302 (02) :769-786

[6] The classification of Dirichletsch's series through their functional comparison. [J].

Hecke, E .

MATHEMATISCHE ANNALEN, 1936, 112 :664-699

[7] Power subgroups of some Hecke groups [J].

Ikikardes, Sebahattin ;

Koruoglu, Ozden ;

Sahin, Recep .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2006, 36 (02) :497-508

[8]

JONES GA, 1986, J LOND MATH SOC, V34, P26

[9]

Knopp MI, 1996, ACTA ARITH, V76, P227

[10] AN ARITHMETIC-GEOMETRIC METHOD IN THE STUDY OF THE SUBGROUPS OF THE MODULAR GROUP [J].

KULKARNI, RS .

AMERICAN JOURNAL OF MATHEMATICS, 1991, 113 (06) :1053-1133

← 1 2 3 →