Huppert's Conjecture for Alternating groups

TL;DR

This paper proves Huppert's Conjecture for alternating groups, showing they are uniquely identified by their irreducible complex representation degrees, confirming a long-standing hypothesis in group theory.

Contribution

The paper establishes that alternating groups of degree at least 5 are uniquely characterized by their irreducible representation degrees, confirming Huppert's Conjecture for these groups.

Findings

Alternating groups of degree ≥ 5 are uniquely determined by their irreducible representation degrees.

Huppert's Conjecture is confirmed for all alternating groups.

The result holds up to an abelian direct factor.

Abstract

We prove that the alternating groups of degree at least $5$ are uniquely determined up to an abelian direct factor by the degrees of their irreducible complex representations. This confirms Huppert's Conjecture for alternating groups.