Speaker:

Anton Evseev (QMUL)

Date/Time:

Mon, 01/03/2010 - 16:30

Room:

M103

Seminar series:

Let G be a
finite group and N be the normalizer of a Sylow p-subgroup of G. The
McKay conjecture, which 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 version due to
Isaacs and Navarro suggests the existence of a correspondence between
irreducible character degrees of G and of N modulo p and up to sign, if
one considers only characters of p'-degree. I will review these
conjectures and will discuss a possible new refinement, which implies
the Isaacsâ€”Navarro conjecture.