Seminar Announcement Date: Wednesday, 21 February 2024 Time: 3:30 PM. Venue: Seminar Hall What Galois might have done had he lived a few years more. P. Vanchinathan VIT Chennai. 210224 Abstract
A finite algebraic F(alpha) over F is a Galois extension if all the conjugates of alpha are in K. When it is not Galois, textbooks don't discuss how many of the conjugates of alpha are in F(alpha). For example this number is a divisor of the degree of the extension. Alexander Pelris gives a simple interpretation for this number in terms of the Galois group of the Galois closure. We will discuss Alexander Perlis' work that says it is possible to construct finite extensions Q(alpha) of Q of degree n with d conjugates alpha in it for a given n and divisor d. After describing this we outline our alternative much elementary proof of this through our "Cluster Magnification Theorem" We assume nothing beyond Undergraduate Algebra.
