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CATEGORIES:Junior Algebra and Number Theory seminar
SUMMARY:The McKay conjecture and Brauer's induction theore
m - Anton Evseev
DTSTART;TZID=Europe/London:20091030T140000
DTEND;TZID=Europe/London:20091030T150000
UID:TALK21223AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/21223
DESCRIPTION:Let G be a finite group and N be the normalizer of
a Sylow p-subgroup of G. The McKay conjecture\, w
hich has been open for more than 30 years\, states
that G and N have the same number of irreducible
characters of degree not divisible by p (i.e. of p
'-degree). The conjecture has been strengthened in
a number of ways. In particular\, a refinement du
e to Isaacs and Navarro suggests a precise corres
pondence between irreducible character degrees of
G and of N modulo p and up to sign\, if one consid
ers only characters of p'-degree. I will review th
ese statements and will present a possible new ref
inement\, which implies the Isaacs-Navarro conject
ure. The talk will be (reasonably) self-contained\
, and the conjectures will be illustrated by a num
ber of "small" examples.
LOCATION:MR13
CONTACT:Anton Evseev
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