The McKay conjecture and Brauer's induction theorem

Anton Evseev

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
163 Downloads (Pure)

Abstract

Let G be an arbitrary finite group. The McKay conjecture asserts that G and the normalizer NG (P) of a Sylow p-subgroup P in G have the same number of characters of degree not divisible by p (that is, of p′-degree). We propose a new refinement of the McKay conjecture, which suggests that one may choose a correspondence between the characters of p′-degree of G and NG (P) to be compatible with induction and restriction in a certain sense. This refinement implies, in particular, a conjecture of Isaacs and Navarro. We also state a corresponding refinement of the Broué abelian defect group conjecture. We verify the proposed conjectures in several special cases.
Original languageEnglish
Pages (from-to)1248-1290
JournalLondon Mathematical Society. Proceedings
Volume106
Issue number6
Early online date4 Jan 2013
DOIs
Publication statusPublished - Jun 2013

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