Abstract
The authors prove the 1990 conjecture of Guralnick and Thompson on composition factors of monodromy groups. Using Riemann's existence theorem, the conjecture translates into a problem on primitive permutation groups. This group theoretic problem had been reduced to a question about actions of classical groups on subspaces of their natural modules. The key ingredients in the present proof are the authors' earlier fixed point ratio estimates for such actions and a result of Scott on the generation of linear groups.
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