Constructing extensions of number fields with dihedral Galois group

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• Alex Chmelnitzki
• Wednesday 06 February 2008, 14:00-15:00
• MR4, CMS, Wilberforce Road, Cambridge, CB3 0WB.

If you have a question about this talk, please contact Anton Evseev.

In this talk I will prove that given a quadratic extension K of the rational numbers and a prime p, there exist infinitely many Galois extension F/K of degree p such that F/Q is also Galois with dihedral Galois group of order 2p. Moreover, F can be chosen such that arbitrarily many primes ramify in F/K. I will only assume familiarity with Galois theory and some basic theory of number fields (in particular ramification of primes) on the level of a standard undergraduate course. We will use class field theory for the construction but I will state all the results we need.

This talk is part of the Junior Algebra and Number Theory seminar series.

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