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- Title
Triangle groups and PSL<sub>2</sub>( q).
- Authors
Marion, Claude
- Abstract
We consider hyperbolic triangle groups of the form T = T p1, p2, p3, where p1, p2, p3 are prime numbers. Let p be a prime number and n be a positive integer. We give a necessary and sufficient condition for L2( pn) to be the image of a given hyperbolic triangle group, where L2( pn) denotes the projective special linear group PSL2( pn). It follows that, given a prime number p, there exists a unique positive integer n such that L2( pn) is the image of a given hyperbolic triangle group. Finally, given a hyperbolic triangle group T, we determine the asymptotic probability that a randomly chosen homomorphism φ : T → L2( pn) is surjective, as pn tends to infinity.
- Subjects
TRIANGLES; PRIME numbers; GROUP theory; HOMOMORPHISMS; MATHEMATICAL functions
- Publication
Journal of Group Theory, 2009, Vol 12, Issue 5, p689
- ISSN
1433-5883
- Publication type
Article
- DOI
10.1515/JGT.2009.004