Résume | Abstract. Let G be a finite group and H be the normaliser of a Sylow p-subgroup of G. The McKay conjecture, which has been open for more than 30 years, asserts that G and H have the same number of irreducible characters of degrees not divisible by p (i.e. of p'-degrees). The conjecture has been strengthened in a number of ways. I will state a possible new refinement, which suggests that a correspondence between irreducible characters of p'-degrees of G and of H may be chosen to be compatible with induction and restriction, in a certain sense. I will consider this refinement in several special cases and, if time allows, will state a corresponding refinement of the Broué abelian defect group conjecture. |