Premium
The structure of the normalisers of the congruence subgroups of the Hecke group G 5
Author(s) -
Lang Mong Lung
Publication year - 2007
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdl001
Subject(s) - mathematics , congruence (geometry) , combinatorics , group (periodic table) , congruence relation , chemistry , geometry , organic chemistry
Let λ = 2cos (π/5) and let τ ∈ ℤ[λ]. Denote the normaliser of G 0 (τ) of the Hecke group G 5 in PSL 2 (ℝ) by N ( G 0 (τ)). Then N ( G 0 (τ)) = G 0 (τ/ h ), where h is the largest divisor of 4 such that h 2 divides τ. Further, N ( G 0 (τ))/ G 0 (τ) is either 1 (if h = 1), ℤ 2 × ℤ 2 (if h = 2) or ℤ 4 × ℤ 4 (if h = 4).