On alternating and symmetric groups as Galois groups
The main result of the paper under review states that the alternating group \(A_n,n\geq 3\) appears as Galois group over any Hilbertian fi eld of characteristic \(\neq 2\). In characteristic 2 the same statement holds for odd \(n\). The proof uses Newton polygons. It is further shown, that any quadratic extension of Hilbertian fields of characteristic different from 2 can be embedded in an \(S_n\)-extension.
scientific article; zbMATH DE number 2108113