Seminario di Algebra e Teoria dei numeri - Solvable primitive extensions

Friday, December 1, 2017
Chandan Dalawat
Harish-Chandra Research Institute

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. We show that a solvable primitive extension E of F is uniquely determined (up to F-isomorphism) by Ê and characterise the extensions D of F such that D=Ê for some solvable primitive extension E of F.  Not much mathematical background will be assumed.