Triangle generation of finite exceptional groups of low rank

Marion, Claude2011-12-162011-12-162011-12-16201110.1016/j.jalgebra.2010.12.005https://infoscience.epfl.ch/handle/20.500.14299/74335WOS:000288353300003Given a triple (p(1), p(2), p(3)) of primes, the object of this paper is the study of the space Hom(T-p1,T-p2,T-p3, G) of homomorphisms from the triangle group T-p1,T-p2,T-p3 to a finite simple exceptional group G of Lie type B-2(2), (2)G(2), G(2) or D-3(4). With a few exceptions, we give precise asymptotic estimates for the size of Hom(T-p1,T-p2,T-p3, G) and determine the limiting probability that a randomly chosen homomorphism from T-p1,T-p2,T-p3 to G is surjective as |G| ---> infinity. (C) 2010 Elsevier Inc. All rights reserved.Finite simple groupsTriangle groupsRandom generationCharacter TablesParabolic SubgroupsTriality GroupsAutomorphism-GroupsMaximal-SubgroupsFuchsian-GroupsG(2)Triangle generation of finite exceptional groups of low ranktext::journal::journal article::research article