# A reduction theorem for the Galois-McKay conjecture

## TL;DR

This paper extends the theory of ordering character triples to include Galois automorphisms, enabling a reduction of the Galois-McKay conjecture to a problem involving simple groups.

## Contribution

It generalizes the ordering character triples theory to Galois actions, facilitating the reduction of the Galois-McKay conjecture to simple group cases.

## Key findings

- Reduced the Galois-McKay conjecture to simple groups
- Extended character triple ordering to Galois automorphisms
- Built on previous work of Ladisch and Turull

## Abstract

We generalize the theory of ordering character triples, developed by Navarro and Sp\"ath, by taking into account the action of Galois automorphisms on characters. This new technique, together with previous results of Ladisch and Turull, allows us to reduce the Galois--McKay conjecture to a question about simple groups.