Solutions explicites de problèmes de plongement. (Explicit solutions of imbedding problems)
In this paper, the author intends to give some effective method, which permits us to construct explicit solutions of a special imbedding problem. Namely, let K be a field of characteristic zero containing a primitive p-th root of unity \(\zeta_ p\) for an odd prime p, and L/K be a Galois extension with Galois group G of order \(p^ d\). Then, he investigates an imbedding problem of L/K with kernel of order p, i.e. whether for given group of order p, identified with \(\mu_ p=<\zeta_ p>\), and cohomological class \(\epsilon \in H^ 2(G,\mu_ p)\), there exists (or not) a field N such that N/L is of degree p, N/K is Galois and the corresponding Galois group is describable with \(\epsilon\). He first determines formulas given in the simplest case, and next shows that for their generalization to the global case by linearity it is sufficient to provide all solutions in the local cases.
scientific article; zbMATH DE number 3935168