Constructing extensions of number fields with dihedral Galois group
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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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