Seminars and Colloquia
Mathematics
Solvable primitive extensions
Fri, Nov 03, 2017,
04:30 PM to 05:31 PM
at Madhava Hall
Prof. C. S. Dalawat
HRI, Allahabad
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.
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. This problem goes back to Évariste Galois; we show how some recent work complements his insights. Not much mathematical background will be assumed.
