A characterization of some finite simple groups by their character codegrees

Hung P. Tong‐Viet

Mathematische Nachrichten, 2025, vol. 298, issue 4, 1356-1369

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

Date: 2025
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