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

Hongning Wang; Xuning Zhang; Selina Zhang; Michelle Chen

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

Group Theory 2022-11-11 v1

Authors: Hongning Wang , Xuning Zhang , Selina Zhang , Michelle Chen

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 $\Sy_4(4), \U_4(2)$ , $\Sy_4(q)\ (q \geq 4)$ , $\U_4(3)$ , ${}^2\F_4(2)'$ , $\J_3$ , $\G_2(3)$ , $\A_9$ , $\J_2$ , $\PSL(4,3)$ , $\McL$ , $\Sy_4(5)$ , $\G_2(4)$ , $\HS$ , $\ON$ and $\M_{24}$ determines the group up to isomorphism.

Keywords

finite group theory character theory

Cite

@article{arxiv.2211.05287,
  title  = {On the characterization of some non-abelian simple groups using codegree set},
  author = {Hongning Wang and Xuning Zhang and Selina Zhang and Michelle Chen},
  journal= {arXiv preprint arXiv:2211.05287},
  year   = {2022}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2209.02660 by other authors

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

Abstract

Keywords

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