# Computation of Belyi maps with prescribed ramification and applications in Galois theory

@article{Barth2021ComputationOB, title={Computation of Belyi maps with prescribed ramification and applications in Galois theory}, author={D. Barth and A. Wenz}, journal={Journal of Algebra}, year={2021}, volume={569}, pages={616-642} }

Abstract We compute genus-0 Belyi maps with prescribed monodromy groups and verify the computed results. Among the computed examples are almost simple primitive groups that satisfy the well known rational rigidity criterion yielding polynomials with prescribed Galois groups over Q ( t ) . We also give an explicit version of a theorem of Magaard, which predicts all sporadic groups occurring as composition factors of monodromy groups of rational functions.

#### 2 Citations

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We close a gap in the literature by showing that the full covering groups of the Mathieu group M22 and of its automorphism group Aut(M22) occur as the Galois groups of Q-regular Galois extensions of… Expand

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