Abstract
The Galois group of the splitting field of an irreducible binomialx 2e −a overQ is computed explicitly as a full subgroup of the holomorph of the cyclic group of order 2e. The general casex n −a is also effectively computed.
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Jacobson, E.T., Vélez, W.Y. The Galois group of a radical extension of the rationals. Manuscripta Math 67, 271–284 (1990). https://doi.org/10.1007/BF02568433
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DOI: https://doi.org/10.1007/BF02568433