Realisation de produits en couronne comme groupe de Galois de polynomes reciproques et construction de polynomes generiques
This article provides necessary and sufficient conditions for each group of order 32 to be realizable as a Galois group over an arbitrary field. These conditions, given in terms of the number of square classes of the field and the triviality of specific elements in related Brauer groups, are used to derive a variety of automatic realizability results.
Irreducibility over of a special symmetric form in a variables is proved for .
A necessary and sufficient condition is given for reducibility of a symmetric polynomial whose number of variables is large in comparison to degree.