Solutions explicites de problèmes de plongement. (Explicit solutions of imbedding problems)
type: Item
instance of: scholarly article
title: Solutions explicites de problèmes de plongement. (Explicit solutions of imbedding problems)
zbMATH Open document ID: 0584.12022
DOI: 10.1016/0022-314X(85)90024-1
author: Richard Massy
published in: Journal of Number Theory
publication date: 1985-01-01T00:00:00Z
review text: 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.
reviewed by: Hideo Yokoi
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 12G05
Mathematics Subject Classification ID: 11R34
zbMATH DE Number: 3935168
zbMATH Keywords: prescribed Galois group
zbMATH Keywords: imbedding problem
MaRDI profile type: Publication
cites work: Zum Einbettungsproblem.
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description: scientific article; zbMATH DE number 3935168