Generators of Fuchsian groups

Small Generators of Cocompact Arithmetic Fuchsian Groups

In the study of Fuchsian groups, it is a nontrivial problem to determine a set of generators. Using a dynamical approach we construct for any cocompact arithmetic Fuchsian group a fundamental region in SL2(R) from which we determine a set of small generators.

Fuchsian Groups: Intro

In various ways, mathematicians associate extra structure with sets and then investigate these objects. For example, by adding a binary operation to a set and validating that the set with the binary operation fulfills certain axioms, we arrive at a group. Similarly, given a set, one can specify a collection of subsets fulfilling some criteria that gives a topology, a sense of which points are c...

Maximal Fuchsian Groups

1. DEFINITIONS. Let D be the unit disk {z\ \z\ < l } and let £ be the group of conformai homeomorphisms of D. A Fuchsian group is a discrete subgroup of <£. We shall be concerned here with the finitely generated Fuchsian groups. It is known that these have the following presentations. Generators: aïy bi, • • • , ag, bg, eh • • • , ek, fa, • • • , hm, pu • * * , pr. Defining relations : e? = eg ...

Compact Deformations of Fuchsian Groups

Alternating Quotients of Fuchsian Groups

It all started with a theorem of Miller [14]: the classical modular group PSL2Z‘ has among its homomorphic images every alternating group, except A6; A7; and A8. In the late 1960s Graham Higman conjectured that any (finitely generated non-elementary) Fuchsian group has among its homomorphic images all but finitely many of the alternating groups. This reduces to an investigation of the cocompac...