The normal subgroup structure of the extended Hecke groups期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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The normal subgroup structure of the extended Hecke groups

Authors:	Özden Koruoğlu Recep Sahin Sebahattin İkikardes

Institution:	1.Bal?kesir üniversitesi Necatibey E?itim Fakültesi, Ilk??retim B?lümü, Matematik E?itimi,Bal?kesir,TüRKIYE;2.Bal?kesir üniversitesi Fen-Edebiyat Fakültesi, Matematik B?lümü,Bal?kesir,TüRKIYE

Abstract:	We consider the extended Hecke groups $\ifmmode\expandafter\bar\else\expandafter\=\fi{H}{\left( \lambda \right)}$ generated by T(z) = −1/z, S(z) = −1/(z + λ) and R(z) = 1/z with λ ≥ 2. In this paper, firstly, we study the fundamental region of the extended Hecke groups $\ifmmode\expandafter\bar\else\expandafter\=\fi{H}{\left( \lambda \right)}$ . Then, we determine the abstract group structure of the commutator subgroups ${\ifmmode\expandafter\bar\else\expandafter\=\fi{H}}\ifmmode{'}\else$'$\fi{\left( \lambda \right)}$ , the even subgroup $\ifmmode\expandafter\bar\else\expandafter\=\fi{H}_{e} {\left( \lambda \right)}$ , and the power subgroups $\ifmmode\expandafter\bar\else\expandafter\=\fi{H}^{m} {\left( \lambda \right)}$ of the extended Hecke groups $\ifmmode\expandafter\bar\else\expandafter\=\fi{H}{\left( \lambda \right)}$ . Also, finally, we give some relations between them.

Keywords:	extended Hecke group fundamental region commutator subgroup even subgroup power subgroup
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