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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Homomorphisms of cocompact Fuchsian groups on $ {\rm PSL}\sb{2}(Z\sb{p\sp{n}}[x]/(f(x)))$

Author: Jeffrey Cohen
Journal: Trans. Amer. Math. Soc. 281 (1984), 571-585
MSC: Primary 20H10; Secondary 11F06
MathSciNet review: 722763
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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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Keywords: Cocompact Fuchsian group, noncongruence subgroup of the modular group, Hurwitz group, simple factor, factor with center, matrix group over $ {Z_{{p^n}}}[x]$
Article copyright: © Copyright 1984 American Mathematical Society

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