Finite Abelian Groups and Rational Galois Extensions

Paul Gilmartin (University of Glasgow)

Thursday 9th May, 2013 16:00-17:00 Maths 516


The "Inverse Galois Problem" is a famous unsolved question in algebra, which asks whether or not, given any finite group A, if there is a Galois extension of the rationals whose Galois group is isomophic to A. If such an extension exists, we say "A can be realised as a rational Galois extension". We consider a less general case, presenting a proof that any finite abelian group can be realised as a rational Galois extension. All definitions and results relevant to the proof will be explained (briefly) beforehand.

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