Huppert's analogue conjecture for $\PSL(3,q)$ and $\PSU(3,q)$

TL;DR

This paper proves that the set of codegrees uniquely identifies the groups $ ext{PSL}(3,q)$ and $ ext{PSU}(3,q)$ among finite groups, extending the analogue conjecture for these groups.

Contribution

It establishes that the codegree set characterizes $ ext{PSL}(3,q)$ and $ ext{PSU}(3,q)$ up to isomorphism, confirming a specific case of Huppert's analogue conjecture.

Findings

Codegree sets determine $ ext{PSL}(3,q)$ and $ ext{PSU}(3,q)$ uniquely.

The result extends the understanding of group invariants in character theory.

Supports the broader conjecture relating codegrees to group structure.

Abstract

Let $G$ be a finite group and $\chi\in \irr(G)$. The codegree of $\chi$ is defined as $\cod(\chi)=\frac{|G:\ker(\chi)|}{\chi(1)}$ and $\cod(G)=\{\cod(\chi) \ |\ \chi\in \irr(G)\}$ is called the set of codegrees of $G$. In this paper, we show that the set of codegrees of $\PSL(3,q)$ and $\PSU(3,q)$ determines the group up to isomorphism.