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INDIAN INSTITUTE OF SCIENCE EDUCATION AND RESEARCH (IISER) PUNE
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An Autonomous Institution, Ministry of Human Resource Development, Govt. of India
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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.

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