Weyl groups as Galois groups of a regular extension of the field \(\mathbb{Q}\)
It is proved that all Weyl groups except those of type \(F_4\) are realized as Galois groups of a regular extension of the rational function field \(\mathbb{Q} (T)\). The author uses a uniform method to find a rigid rational triplet for each Weyl group (except those of types \(D_{2k}\) and \(F_4\)) and the results of \textit{G. V. Belyi} [Izv. Akad. Nauk SSSR, Ser. Mat. 43, 267-276 (1979; Zbl 0409.12012)]. Remark that the Weyl group of type \(F_4\), excluded from the main theorem, is solvable.
scientific article; zbMATH DE number 907270
scientific article