Abstract
Given a triple ( p 1 , p 2 , p 3 ) of primes, the object of this paper is the study of the space Hom ( T p 1 , p 2 , p 3 , G ) of homomorphisms from the triangle group T p 1 , p 2 , p 3 to a finite simple exceptional group G of Lie type B 2 2 , G 2 2 , G 2 or D 4 3 . With a few exceptions, we give precise asymptotic estimates for the size of Hom ( T p 1 , p 2 , p 3 , G ) and determine the limiting probability that a randomly chosen homomorphism from T p 1 , p 2 , p 3 to G is surjective as | G | → ∞ .
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