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We obtain conditions under which PSL2(Z.»[*]/(/(■*))) is a factor of ( /, m, n ). Using this, certain results about factors of cocompact Fuchsian groups are obtained. For example, it is shown that: (i) T has infinitely many simple nonabelian factors. (ii) T has factors with nontrivial center. (iii) For each n, there exists m such that T has at least n factors of order m. Further, all factored normal subgroups can be taken torsion-free. Also, new Hurwitz groups and noncongruence subgroups of the modular group are obtained.

Homomorphisms of cocompact Fuchsian groups on 𝑃𝑆𝐿₂(𝑍_{𝑝ⁿ}[𝑥]/(𝑓(𝑥)))