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

Cohen, Jeffrey

doi:10.1090/S0002-9947-1984-0722763-3

Homomorphisms of cocompact Fuchsian groups on $\textrm {PSL}_{2}(Z_{p^{n}}[x]/(f(x)))$
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Trans. Amer. Math. Soc. 281 (1984), 571-585 Request permission

Abstract:

We obtain conditions under which ${\text {PSL}}_2({Z_{{p^n}}}[x]/(f(x)))$ is a factor of $(l,m,n)$. Using this, certain results about factors of cocompact Fuchsian groups are obtained. For example, it is shown that: (i) $\Gamma$ has infinitely many simple nonabelian factors. (ii) $\Gamma$ has factors with nontrivial center. (iii) For each $n$, there exists $m$ such that $\Gamma$ 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.

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