We identify the normal subgroups of the orientation preserving subgroup [3, 5, 3] of the Coxeter group [3, 5, 3], with the factor group isomorphic to PSL2(Fq) with particular congruence subgroups of an arithmetic subgroup of PSL2(C) derived from a quaternion algebra over a quartic field. 1 Motivation – Hurwitz groups and HurwitzMacbeath surfaces It is a well known fact that up to isomorphy, the...

Let Mg,n and Hg,n, for 2g − 2 + n > 0, be, respectively, the moduli stack of n-pointed, genus g smooth curves and its closed substack consisting of hyperelliptic curves. Their topological fundamental groups can be identified, respectively, with Γg,n and Hg,n, the so called Teichmüller modular group and hyperelliptic modular group. A choice of base point on Hg,n defines a monomorphism Hg,n →֒ Γg,...

A subgroup of V containing a principal congruence subgroup T(«) is said to be a congruence subgroup, and is of level « if « is the least such integer. In a recent article [2] the writer determined all normal subgroups of T of genus 1 (see [l] for the definition of the genus of a subgroup of r). An interesting question that arises is to decide which of these are also congruence subgroups. In thi...

In this paper, we generalize some results related to the congruence subgroups of modular group ; given in [7] and [6] by Kiming, Schütt, and Verrill, to the extended modular group ̆: 2010 Mathematics Subject Classification: 11F06

In the present note we characterize finite lattices which are isomorphic to the congruence lattice of an abelian lattice ordered group.