Vol. 70, No. 2, 1977

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Normal congruence subgroups of the Hecke groups G(2(12)) and G(3(12))

L. Alayne Parson

Vol. 70 (1977), No. 2, 481–487
Abstract

NormaI congruence subgroups of the classical modular group have been completely classifled by M. Newman and D. McQuillan. In this note we begin the classification of normal congruence subgroups of the Hecke groups G(2(12)) and G(3(12)).

Our main result is that if G is a normal congruence subgroup of G(m(12)), m = 2,3, containing the principal congruence subgroup Γm(nm(12)) where (n,6) = 1 and if G contains only even elements, then G is Γm(dm(12)), Γm(dm(12)) where dn or Γm(d), Γm(d) where dn and d > 1. To obtain this result we use facts about the level of a congruence subgroup which are of independent interest.

Mathematical Subject Classification 2000
Primary: 10D05, 10D05
Secondary: 20H10
Milestones
Received: 22 December 1976
Revised: 28 April 1977
Published: 1 June 1977
Authors
L. Alayne Parson