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The McKay conjecture and Brauer's induction theorem

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If you have a question about this talk, please contact Anton Evseev.

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 refinement due to Isaacs and Navarro suggests a precise 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 statements and will present a possible new refinement, which implies the Isaacs-Navarro conjecture. The talk will be (reasonably) self-contained, and the conjectures will be illustrated by a number of “small” examples.

This talk is part of the Junior Algebra and Number Theory seminar series.

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