A CLASSIFICATION OF SURDS OF NON-ARITHMETICAL GROUPS

Definitions and classifications of reduced surds for non-arithmetical groups on the hyperbolic plane is proposed, as well those some congruence subgroups. The considered are desymmetrized group, its Γ0 subgroup, a generalized Hecke group according choice commutator subgroup group. definitions studied to ordering generators conjugacy subclasses groups. construction tori defined obtained after tessellation Upper Hyperbolic Half Plane discussed. Cutting trajectories cutting-trajectories sequences uniquely new definition surds.