On the characterization of some non-abelian simple groups using codegree set

Abstract

Let G be a finite group and $\chi \in \text{Irr}(G)$. The codegree of χ is defined as $\text{cod}(\chi )=|G:\mathrm{\text{ker}}(\chi )|/\chi (1)$ and $\text{cod}(G)=\{\text{cod}(\chi )|\chi \in \text{Irr}(G)\}$ is called the set of codegrees of G. In this paper, we show that the set of codegrees of ${\mathsf{U}}_4(2),{\mathsf{S}}_4(q)(q=2^f\ge 4),{\mathsf{U}}_4(3),{}^2{\mathsf{F}}_4(2)\prime ,{\mathsf{J}}_3,{\mathsf{G}}_2(3),{\mathsf{A}}_9,{\mathsf{J}}_2,\text{PSL}(4,3),\text{McL},{\mathsf{S}}_4(5),{\mathsf{G}}_2(4),\text{HS},\mathrm{O}\prime \mathrm{N}$ and ${\mathsf{M}}_{24}$ determines the group up to isomorphism.

KEYWORDS:

• $\text{cod}(G)=\{\text{cod}(\chi )|/\chi \in \text{Irr}(G)$
• finite group
• isomorphism $r(\chi )|/\chi (1)$
• $\chi \in \text{Irr}(G)$

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 20C15

Acknowledgments

The authors are grateful to the referee for the valuable suggestions that greatly improved the manuscript.