The Navarro Conjecture for the alternating groups

TL;DR

This paper proves Navarro's strengthened McKay conjecture for alternating groups when the prime is odd, advancing understanding of the conjecture's validity in specific group cases.

Contribution

The paper establishes the Navarro conjecture for alternating groups for all odd primes, providing a significant step in the conjecture's verification.

Findings

Navarro conjecture holds for alternating groups with odd primes

Advances the understanding of the McKay conjecture

Provides proof for a specific class of groups

Abstract

Recently Navarro proposed a strengthening of the unsolved McKay conjecture using Galois automorphisms. We prove that the Navarro conjecture holds for the alternating groups when the prime p is odd.