On the characterization of some non-abelian simple groups with few codegrees

Abstract

Let G be a finite group and $\chi \in \text{Irr}(G).$ The codegree of χ is defined as $\text{cod}(\chi )=\frac{|G:\ker (\chi )|}{\chi (1)}$ 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 $M_{11},M_{12},M_{22},M_{23},$ and $\text{PSL}(3,3)$ determines the group up to isomorphism.

Keywords:

• Character degree, character codegree
• simple group

2020 Mathematics Subject Classification:

• 20C15

Acknowledgments

The authors thank Texas State University for providing a great working environment and support. The authors are also grateful to the referee for the valuable suggestions and comments.

Additional information

Funding

This research was conducted under NSF-REU grant DMS-1757233 and NSA grant H98230-21-1-0333 by Gintz, Kortje, Laurence, and Wang during the Summer of 2021 under the supervision of Liu and Yang. The authors gratefully acknowledge the financial support of NSF and NSA. Liu was partially supported by NSFC (Grant Nos. 11701421 and 11871011) and the Science & Technology Development Fund of Tianjin Education Commission for Higher Education (2020KJ010). Yang was also partially supported by a grant from the Simons Foundation (#499532).