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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:On the Chebotarev invariant of a finite group - Ga
reth Tracey (University of Bath)
DTSTART;TZID=Europe/London:20200114T110000
DTEND;TZID=Europe/London:20200114T120000
UID:TALK136627AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/136627
DESCRIPTION:Given a \;nite group X\, a classical approach
to proving that X is the Galois groupof a Galois e
xtension K=Q can be described roughly as follows:
(1) prove that Gal(K=Q) iscontained in X by using
known properties of the extension (for example\, t
he Galois group of anirreducible polynomial f(x) 2
Z[x] of degree n embeds into the symmetric group
Sym(n))\; (2)try to prove that X = Gal(K=Q) by com
puting the Frobenius automorphisms modulo successi
veprimes\, which gives conjugacy classes in Gal(K=
Q)\, and hence in X. If these conjugacy classescan
only occur in the case Gal(K=Q) = X\, then we are
done. The Chebotarev invariant of Xcan roughly be
described as the e\;ciency of this algorithm"
.In this talk we will de\;ne the Chebotarev in
variant precisely\, and describe some new resultsc
oncerning its asymptotic behaviour.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:INI IT
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