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SUMMARY:Constructing extensions of number fields with dihedral Galois grou
 p - Alex Chmelnitzki
DTSTART:20080206T140000Z
DTEND:20080206T150000Z
UID:TALK10675@talks.cam.ac.uk
CONTACT:Anton Evseev
DESCRIPTION:In this talk I will prove that given a quadratic extension K o
 f\nthe rational numbers and a prime p\, there exist infinitely many Galois
 \nextension F/K of degree p such that F/Q is also Galois with dihedral Gal
 ois\ngroup of order 2p. Moreover\, F can be chosen such that arbitrarily m
 any\nprimes ramify in F/K. I will only assume familiarity with Galois theo
 ry and\nsome basic theory of number fields (in particular ramification of 
 primes)\non the level of a standard undergraduate course. We will use clas
 s field\ntheory for the construction but I will state all the results we n
 eed.
LOCATION:MR4\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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