Carolina Vallejo (Valencia)

p-rational characters and p-decomposable Sylow normalizers.

Abstract:

It has been conjectured by G. Navarro that if p is an odd prime, then a group G has a p-decomposable Sylow p-subgroup normalizer iff the only p'-degree p-rational character in the principal block of G is the trivial one. Using a McKay type natural correspondence between characters in the principal blocks of G and N_G(P) where P is a Sylow p-subgroup of G, we can prove half of this conjecture. (Join work with G.Navarro and P. H. Tiep).