The structure of the normalisers of the congruence subgroups of the Hecke group G5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 structure of the normalisers of the congruence subgroups of the Hecke group G5

Authors:	Lang Mong Lung

Institution:	Department of Mathematics National University of Singapore Singapore 117543 matlml{at}math.nus.edu.sg

Abstract:	Let ${lambda}$ = 2cos ( ${pi}$ /5) and let ${tau}$ $isin$ $Z$ ${lambda}$ ]. Denote the normaliser ofG₀( ${tau}$ ) of the Hecke group G₅ in PSL₂( $R$ ) by N(G₀( ${tau}$ )). Then N(G₀( ${tau}$ ))= G₀( ${tau}$ /h), where h is the largest divisor of 4 such that h² divides ${tau}$ . Further, N(G₀( ${tau}$ ))/G₀( ${tau}$ ) is either 1 (if h = 1), $Z$ ₂ x $Z$ ₂ (if h= 2) or $Z$ ₄ x $Z$ ₄ (if h = 4).

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