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

Abstract

Let λ = 2cos (π/5) and let τ ∈ ℤ[λ]. Denote the normaliser of G0(τ) of the Hecke group G5 in PSL2(ℝ) by N(G0(τ)). Then N(G0(τ)) = G0(τ/h), where h is the largest divisor of 4 such that h 2 divides τ. Further, N(G0(τ))/G 0(τ) is either 1 (if h = 1), ℤ2 × ℤ2 (if h = 2) or ℤ4 × ℤ4 (if h = 4). © 2006 London Mathematical Society.