## Seminario di Algebra e Teoria dei numeri - Solvable primitive extensions

**Abstract**: A finite separable extension E of a field F is called primitive if there are no intermediate extensions. It is called solvable if the group Gal(Ê |F) of automorphisms of its galoisian closure Ê over F is solvable. What are the solvable primitive extensions of F ? This problem goes back to Évariste Galois; we show how some recent work complements his insights.