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Bulletin of the London Mathematical Society Advance Access originally published online on December 15, 2006
Bulletin of the London Mathematical Society 2007 39(1):53-62; doi:10.1112/blms/bdl001
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© 2006 London Mathematical Society

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

Mong Lung Lang

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

Received 8 July 2005. Revision received 23 March 2006.

Let {lambda} = 2cos ({pi}/5) and let {tau} isin Z[{lambda}]. Denote the normaliser of G0({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), Z2 x Z2 (if h = 2) or Z4 x Z4 (if h = 4).


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