Abstract: We extend the results of Garbe [3], Macbeath [4] and
Sinkov [7] to classify all epimorphisms We obtain a complete
set of conditions under which is a factor
group of any
chosen finite or infinite triangle group.
Keywords and phrases: special projective linear groups, projective general linear groups, Fuchsian groups, homomorphisms, automorphisms, triangle groups, Galois fields, admissible characteristics, presentations.