McKay natural correspondences on characters

Let [math] be a finite group, let [math] be an odd prime, and let [math] . If [math] , then there is a canonical correspondence between the irreducible complex characters of [math] of degree not divisible by [math] belonging to the principal block of [math] and the linear characters of [math] . As a consequence, we give a characterization of finite groups that possess a self-normalizing Sylow [math] -subgroup or a [math] -decomposable Sylow normalizer.

2-Brauer correspondent blocks with one simple module

Abstract One of the main problems in representation theory is to understand the exact relationship between Brauer corresponding blocks of finite groups. The case where the local correspondent has a unique simple module seems key. We study this situation for 2-blocks.

A reduction theorem for the Galois–McKay conjecture

We introduce H {\mathcal {H}} -triples and a partial order relation on them, generalizing the theory of ordering character triples developed by Navarro and Späth. This generalization takes into account the action of Galois automorphisms on characters and, together with previous results of Ladisch and Turull, allows us to reduce the Galois–McKay conjecture to a question about simple groups.

Brauer correspondent blocks with one simple module

One of the main problems in representation theory is to understand the exact relationship between Brauer corresponding blocks of finite groups. The case where the local correspondent has a unique simple module seems key. We characterize this situation for the principal p-blocks where p is odd.

Characters and generation of Sylow 2-subgroups