A characterization of some finite simple groups by their character codegrees

TL;DR

This paper proves that if a finite group shares the same set of character codegrees as a finite simple exceptional Lie type group or a projective special linear group, then the two groups are isomorphic.

Contribution

It characterizes certain finite simple groups uniquely by their character codegree sets, establishing a new identification method.

Findings

Finite simple groups are uniquely determined by their character codegree sets.

Character codegree sets can distinguish between different finite simple groups.

The result applies to exceptional Lie type groups and projective special linear groups.

Abstract

For a finite group $G$ and an irreducible complex character $\chi$ of $G$, the codegree of $\chi$ is defined by $\textrm{cod}(\chi)=|G:\textrm{ker}(\chi)|/\chi(1)$, where $\textrm{ker}(\chi)$ is the kernel of $\chi$. In this paper, we show that if $H$ is a finite simple exceptional group of Lie type or a projective special linear group and $G$ is any finite group such that the character codegree sets of $G$ and $H$ coincide, then $G$ and $H$ are isomorphic.